Industrial Engineering - Operations Research I - Case Study

8/14/2019 Industrial Engineering - Operations Research I - Case Study

1/18

MIDDLE EAST TECHNICAL UNIVERSITY

I E 2 5 1 O P E R A T I O N A L R E S E A R C H I

CASE

STUDY 1


2/18

Contents

PAGE

Introduction.. 2

1. Assumptions..... 2

2. Linear Programming Model.... 3

3. Plans for Production and Sales 5

4. Increasing Graphite or Advertising Cash. 5

5. Adding Extra Packing Machine, Assembly and Labor Hours............................. 6

6. Increasing the Maximum Demand... 7


3/18

Introduction

This report contains detailed production and sales plans for Golf-Sport Company for

two months in accordance with limits that are given in question and assumptions which are

made to clarify ambiguous parts.

In the first part of this report, the assumptions which resemble real life expectations in

conformity with the limits given in the question can be found. Following that, in the second

part, there are plans and recommendations for production and sales of Golf-Sport Company,

including the models used in solving this question. In addition, expected reactions and

forward steps for given changes in constraints could be found in this section.

Finally, in appendix, detailed Excel Solver Sensitivity Report is given for furher

analysis for Golf-Sport Companys production and sales plans.

1. Assumptions


4/18

2. Linear Programming Model

This given model is used in solving Golf-Sport Companys production and sales problem:

Decision Variables and Parameters:

: amount of product i produced on plant j in month t

: amount of sales of product i on plant j in month t

: amount of inventory i produced on plant j at the end of first month

: minimum demand for product i from plant j: maximum demand for product i from plant j

: required labor time per unit for product i on plant j

: required packing time per unit for product i on plant j


5/18

Objective Function:

max z = 2=1 3=1 rijt sijt xijt cijt 9

=1 3=1 (9=1 ivcij i ij )

s.t.:

xij 9

1

pij


6/18

3. Plans for Production and Sales

The tables below show the amount of products should be produced in each month . If

we take a closer look into the tables, it can be clearly seen that, company is better of it does

not produce steel shafts, set - steel, metal or set steel insert in any of two months.

Furthermore, the other components, namely, Graphite shafts, Forged iron heads, Metal Wood

heads, Titanium Insert heads should be produced in all there plants with the same amounts

each month. SetGraphite, metal should be produced only in the plant Tucson; whereas Set -

Graphite, Insert should be produced in all the plants in first month and only in Chandler and

Glendale in the second month. If the company plans its production according to these tables, it

will maximize the profit and meet the demand at the same time.

1st

MONTH Chandler Glendale Tucson 2nd

MONTH Chandler Glendale Tucson

Steel shafts Steel shafts

Graphite shafts 100 100 50 Graphite shafts 100 100 50

Forged iron heads 200 200 100 Forged iron heads 200 200 100

Metal Wood heads 30 30 15 Metal Wood heads 30 30 15


7/18

Name Final Value

Shadow

Price

Constraint

R.H. Side

Allowable

Increase

Allowable

Decrease

Advertising (1st Month) 18450,49771 0 20000 1E+30 1549,502

Advertising (2nd Month) 18262,14624 0 20000 1E+30 1737,854

Graphite (in pounds) (1st Month) 882,8071718 0 1000 1E+30 117,1928

Graphite (in pounds) (2nd Month) 623,4797467 0 1000 1E+30 376,5203

Advertising and Graphite Constraints (Derived from Sensitivity Report (Appendix I)

5. Adding Extra Packing Machine, Assembly and Labor Hours

The table below which is derived from sensitivity report represents the shadow price

and allowable increase about the packing constraints in plants Chandler, Glendale and

Tucson. As the available packing constraint has not been used entirely in Glendale, shadow

price is 0 in each month. Therefore, there is no need for extra packing machine hours in

Glendale. Secondly, in Chandler we are willing to pay less than the shadow price given in the

table below, in other words 1.916666667 per hour for the first month and 1.496667 per hour

for the second month. In order to maintain the same optimal basis, the company can have


8/18

The table above also represents the shadow price and allowable increase about the

assembly time constraints. It can be seen that available amount for assembly time has not

been used entirely in each month on any plants Chandler, Glendale and Tucson. Therefore,

increasing the amount of assembly time will have no effect on the amount of production; as a

result company should not add extra assembly hours on any plant.

Finally, the sensitivity evaluation of labor constraints can be seen in the table below.

On plants Chandler and Tucson, since the available labor is not fully utilized, any labor hour

improvement on these plants will not result any increase in production and also in profit.

Therefore, the company should not add extra labor hours on Chandler and Tucson. In contrast,

it can be seen that on plant Glendale, adding extra labor hours increases the profit by

2.037915 and 1.543128 respectively for each month, thus company would be willing to pay

less than the shadow prices given for extra labor hours within the limits of allowable increase,

3804.259 and 5176.667 respectively in order to increase profit and maintain the same solution

basis at the same time.

LABOR CONSTRAINTS Shadow Price Allowable Increase

Chandler (1st Month) 0 1E+30

Chandler (2nd Month) 0 1E+30


9/18

For the first month:

Name

Final

Value

Shadow

Price

Constraint

R.H. Side

Allowable

Increase

Sales of Titanium Insert heads on Chandler 2000 2,5 2000 580.44776

Sales of Titanium Insert heads on Glendale 2000 5,810427 2000 723

Sales of Graphite shafts on Tucson 2000 0,193705 2000 403

Sales of Titanium Insert heads on Tucson 2000 7,539952 2000 377.8125

Binding Maximum Demand Constraints for First Month (Derived from Sensitivity Report (Appendix I)

In order to check if the company can handle the 50% increase in maximum demand,

the amount of sales which have already reached their maximum levels should be considered,

because any improvement in other non-binding constraints will have no effect on the quantity

of sales. For the first month, it can be seen from the table above, only sales of Titanium Insert

heads on all plants and Graphite shafts on plant Tucson have reached their maximum demand.

For an increase of 50% in maximum demand, only sales of Titanium Insert heads on Chandler

can attain that level without any improvement or allocation in resources, on the other hand

there is a need of more resources for other products or a change in allocation of scarce

resources.


10/18

Secondly, with the same idea mentioned in the previous part, the binding maximum

demand constraints of second month should be analysed as given in the above table. It can be

seen that only Titanium Insert heads on plant Tucson can handle a 50% increase in maximum

demand with current system. For Glendale and Chandler, there must be some improvements

or change in usages of resources to increase the capacity of production.

The effect of each change in maximum demands on the profit can be shown by the

table below (for the second month):

Shadow Price Increase

Effect of this increase on

profit (minimum)

Titanium Insert heads on Chandler 1.9 x 580.4478 = 1102.851

Titanium Insert heads on Glendale 5.40436 x 723 = 3907.352

Titanium Insert heads on Tucson 6.083077 x 1000 = 6083.077

7. ConclusionThe aim of Golf-Sport is to maximize its profit by using the scarce resources most

ffi i tl I d t hi thi t i d t ll t th i t ith th i


11/18

10

APPENDIX

I. Sensitivity Report

Adjustable Cells

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$B$2 Production of Steel shafts on Chandler (1st Month) 0 0 4 2.16 1E+30

$C$2 Production of Steel shafts on Glendale (1st Month) 0 0 5 2.131753555 1E+30

$D$2 Production of Steel shafts on Tucson (1st Month) 0 0 5 2.231680015 1E+30

$B$3 Production of Graphite shafts on Chandler (1st Month) 100 0 6 1.666666667 1E+30

$C$3 Production of Graphite shafts on Glendale (1st Month) 100 0 7 0.132701422 1E+30

$D$3 Production of Graphite shafts on Tucson (1st Month) 2000 0 10 3.271680015 0.1937046

$B$4 Production of Forged iron heads on Chandler (1st Month) 200 0 4 2.42 1E+30$C$4 Production of Forged iron heads on Glendale (1st Month) 200 0 3 2.626540284 1E+30

$D$4 Production of Forged iron heads on Tucson (1st Month) 100 0 5 2.294570684 1E+30

$B$5 Production of Metal Wood heads on Chandler (1st Month) 30 0 8 3.32 1E+30

$C$5 Production of Metal Wood heads on Glendale (1st Month) 30 0 7 2.170616114 1E+30

$D$5 Production of Metal Wood heads on Tucson (1st Month) 15 0 10 1.113801453 1E+30

$B$6 Production of Titanium Insert heads on Chandler (1st Month) 2000 0 14 4.6 2.5

$C$6 Production of Titanium Insert heads on Glendale (1st Month) 2000 0 16 4.393933649 5.81042654

$D$6 Production of Titanium Insert heads on Tucson (1st Month) 2000 0 18 3.943125349 7.539951574

$B$7 Production of Set - Steel, Metal on Chandler (1st Month) 0 0 112 64.64 1E+30

$C$7 Production of Set - Steel, Metal on Glendale (1st Month) 0 0 115 65.45781991 1E+30

$D$7 Production of Set - Steel, Metal on Tucson (1st Month) 0 0 130 60.76125908 1E+30

$B$8 Production of Set - Steel Insert on Chandler (1st Month) 0 0 152 68.64 1E+30

$C$8 Production of Set - Steel Insert on Glendale (1st Month) 0 0 160 55 1E+30

$D$8 Production of Set - Steel Insert on Tucson (1st Month) 0 0 180 65.22692308 1E+30


12/18

11

$B$9 Production of Set - Graphite, Metal on Chandler (1st Month) 0 0 210 20 1E+30

$C$9 Production of Set - Graphite, Metal on Glendale (1st Month) 0 0 200 11.94312796 1E+30

$D$9 Production of Set - Graphite, Metal on Tucson (1st Month) 0 0 270 1.96125908 1E+30

$B$10 Production of Set - Graphite, Insert on Chandler (1st Month) 53.5 0 230 50 20

$C$10 Production of Set - Graphite, Insert on Glendale (1st Month) 34.26540284 0 215 122.6 4

$D$10 Production of Set - Graphite, Insert on Tucson (1st Month) 14.63680387 0 270 5.333333333 1.947115385

$M$4 Production of Steel shafts on Chandler (2nd Month) 0 0 3.28 2.706666667 2.16

$N$4 Production of Steel shafts on Glendale (2nd Month) 0 0 4.4 1.000947867 2.131753555

$O$4 Production of Steel shafts on Tucson (2nd Month) 0 0 4.16 3.974615385 2.231680015

$M$5 Production of Graphite shafts on Chandler (2nd Month) 100 0 3.72 2.266666667 3.2

$N$5 Production of Graphite shafts on Glendale (2nd Month) 100 0 4.84 0.560947867 3.171753555

$O$5 Production of Graphite shafts on Tucson (2nd Month) 50 0 7.6 0.534615385 3.271680015

$M$6 Production of Forged iron heads on Chandler (2nd Month) 200 0 3.52 3.963333333 2.42

$N$6 Production of Forged iron heads on Glendale (2nd Month) 200 0 2.4 4.544075829 2.626540284

$O$6 Production of Forged iron heads on Tucson (2nd Month) 100 0 4.4 4.819230769 2.294570684$M$7 Production of Metal Wood heads on Chandler (2nd Month) 30 0 6.8 2.18 3.32

$N$7 Production of Metal Wood heads on Glendale (2nd Month) 30 0 5.68 1.264075829 3.106540284

$O$7 Production of Metal Wood heads on Tucson (2nd Month) 15 0 8.56 0.659230769 2.854570684

$M$8 Production of Titanium Insert heads on Chandler (2nd Month) 2000 0 10.88 1E+30 1.9

$N$8 Production of Titanium Insert heads on Glendale (2nd Month) 2000 0 13.12 1E+30 4.393933649

$O$8 Production of Titanium Insert heads on Tucson (2nd Month) 2000 0 14.76 1E+30 3.943125349

$M$9 Production of Set - Steel, Metal on Chandler (2nd Month) 0 0 90.64 88.96 64.64

$N$9 Production of Set - Steel, Metal on Glendale (2nd Month) 0 0 94 66.48530806 65.45781991

$O$9 Production of Set - Steel, Metal on Tucson (2nd Month) 0 0 108.4 117.2 60.76125908

$M$10 Production of Set - Steel Insert on Chandler (2nd Month) 0 0 124.64 54.96 68.64

$N$10 Production of Set - Steel Insert on Glendale (2nd Month) 0 0 133.6 29.2 69.8

$O$10 Production of Set - Steel Insert on Tucson (2nd Month) 0 0 151.2 72.77307692 65.22692308

$M$11 Production of Set - Graphite, Metal on Chandler (2nd Month) 0 0 168 11.6 78.4

$N$11 Production of Set - Graphite, Metal on Glendale (2nd Month) 0 0 156.8 3.685308057 80.25781991


13/18

12

$O$11 Production of Set - Graphite, Metal on Tucson (2nd Month) 84.84375 0 225.6 56.14949437 8.030992736

$M$12 Production of Set - Graphite, Insert on Chandler (2nd Month) 53.5 0 179.6 38 11.6

$N$12 Production of Set - Graphite, Insert on Glendale (2nd Month) 34.26540284 0 162.8 61.57777778 3.738461538

$O$12 Production of Set - Graphite, Insert on Tucson (2nd Month) 0 0 216 7.973076923 82.02692308

$B$109 Inventory of Steel shafts on Chandler (end of the 1st Month) 0 -2.16 -1.2 2.16 1E+30

$C$109 Inventory of Steel shafts on Glendale (end of the 1st Month) 0 -2.131753555 -1 2.131753555 1E+30

$D$109 Inventory of Steel shafts on Tucson (end of the 1st Month) 0 -2.231680015 -1.4 2.231680015 1E+30

$B$110 Inventory of Graphite shafts on Chandler (end of the 1st Month) 0 -3.2 -3.8 3.2 1E+30

$C$110 Inventory of Graphite shafts on Glendale (end of the 1st Month) 0 -3.171753555 -3.6 3.171753555 1E+30

$D$110 Inventory of Graphite shafts on Tucson (end of the 1st Month) 0 -3.271680015 -4 3.271680015 1E+30

$B$111 Inventory of Forged iron heads on Chandler (end of the 1st Month) 0 -2.42 -0.8 2.42 1E+30

$C$111 Inventory of Forged iron heads on Glendale (end of the 1st Month) 0 -2.626540284 -1 2.626540284 1E+30

$D$111 Inventory of Forged iron heads on Tucson (end of the 1st Month) 0 -2.294570684 -1 2.294570684 1E+30

$B$112 Inventory of Metal Wood heads on Chandler (end of the 1st Month) 0 -3.32 -2 3.32 1E+30

$C$112 Inventory of Metal Wood heads on Glendale (end of the 1st Month) 0 -3.106540284 -2.2 3.106540284 1E+30$D$112 Inventory of Metal Wood heads on Tucson (end of the 1st Month) 0 -2.854570684 -2.4 2.854570684 1E+30

$B$113 Inventory of Titanium Insert heads on Chandler (end of the 1st Month) 0 -4.6 -5.2 4.6 1E+30

$C$113 Inventory of Titanium Insert heads on Glendale (end of the 1st Month) 0 -4.393933649 -4.8 4.393933649 1E+30

$D$113 Inventory of Titanium Insert heads on Tucson (end of the 1st Month) 0 -3.943125349 -5.4 3.943125349 1E+30

$B$114 Inventory of Set - Steel, Metal on Chandler (end of the 1st Month) 0 -64.64 -35.6 64.64 1E+30

$C$114 Inventory of Set - Steel, Metal on Glendale (end of the 1st Month) 0 -65.45781991 -35 65.45781991 1E+30

$D$114 Inventory of Set - Steel, Metal on Tucson (end of the 1st Month) 0 -60.76125908 -36 60.76125908 1E+30

$B$115 Inventory of Set - Steel Insert on Chandler (end of the 1st Month) 0 -68.64 -45.6 68.64 1E+30

$C$115 Inventory of Set - Steel Insert on Glendale (end of the 1st Month) 0 -69.8 -44 69.8 1E+30

$D$115 Inventory of Set - Steel Insert on Tucson (end of the 1st Month) 0 -65.22692308 -48 65.22692308 1E+30

$B$116 Inventory of Set - Graphite, Metal on Chandler (end of the 1st Month) 0 -78.4 -70 78.4 1E+30

$C$116 Inventory of Set - Graphite, Metal on Glendale (end of the 1st Month) 0 -80.25781991 -72 80.25781991 1E+30

$D$116 Inventory of Set - Graphite, Metal on Tucson (end of the 1st Month) 0 -75.96125908 -74 75.96125908 1E+30

$B$117 Inventory of Set - Graphite, Insert on Chandler (end of the 1st Month) 0 -84 -84 84 1E+30


14/18

13

$C$117 Inventory of Set - Graphite, Insert on Glendale (end of the 1st Month) 0 -87 -87 87 1E+30

$D$117 Inventory of Set - Graphite, Insert on Tucson (end of the 1st Month) 0 -82.02692308 -90 82.02692308 1E+30

Constraints

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease

$G$13 Labor on Chandler (1st Month) 11027.75 0 12000 1E+30 972.25

$G$14 Packing on Chandler (1st Month) 20000 1.916666667 20000 2509.032258 6420

$G$25 Labor on Glendale (1st Month) 15000 2.037914692 15000 3804.259499 3615

$G$26 Packing on Glendale (1st Month) 23148.95735 0 40000 1E+30 16851.04265

$G$36 Labor on Tucson (1st Month) 19960.454 0 22000 1E+30 2039.546005

$G$37 Packing on Tucson (1st Month) 35000 1.307506053 35000 4129.080882 3022.5

$B$51 Assembly Time on Chandler (1st Month) 3477.5 0 5500 1E+30 2022.5

$C$51 Assembly Time on Glendale (1st Month) 2055.924171 0 5000 1E+30 2944.075829

$D$51 Assembly Time on Tucson (1st Month) 951.3922518 0 6000 1E+30 5048.607748

$A$58 Advertising (1st Month) 18450.49771 0 20000 1E+30 1549.502294

$B$64 Graphite (in pounds) (1st Month) 882.8071718 0 1000 1E+30 117.1928282

$B$95 Sales of Steel shafts on Chandler (1st Month) 0 0 2000 1E+30 2000

$B$96 Sales of Graphite shafts on Chandler (1st Month) 100 0 2000 1E+30 1900

$B$97 Sales of Forged iron heads on Chandler (1st Month) 200 0 2000 1E+30 1800

$B$98 Sales of Metal Wood heads on Chandler (1st Month) 30 0 2000 1E+30 1970

$B$99 Sales of Titanium Insert heads on Chandler (1st Month) 2000 2.5 2000 580.4477612 622.3076923

$B$100 Sales of Set - Steel, Metal on Chandler (1st Month) 0 0 200 1E+30 200

$B$101 Sales of Set - Steel Insert on Chandler (1st Month) 0 0 100 1E+30 100

$B$102 Sales of Set - Graphite, Metal on Chandler (1st Month) 0 0 300 1E+30 300

$B$103 Sales of Set - Graphite, Insert on Chandler (1st Month) 53.5 0 400 1E+30 346.5

$B$95 Sales of Steel shafts on Chandler (1st Month) 0 -3.666666667 0 1605 0

$B$96 Sales of Graphite shafts on Chandler (1st Month) 100 -1.666666667 100 827.2434929 100

$B$97 Sales of Forged iron heads on Chandler (1st Month) 200 -5.583333333 200 1284 200


15/18

14

$B$98 Sales of Metal Wood heads on Chandler (1st Month) 30 -3.5 30 1070 30

$B$99 Sales of Titanium Insert heads on Chandler (1st Month) 2000 0 100 1900 1E+30

$B$100 Sales of Set - Steel, Metal on Chandler (1st Month) 0 -118 0 53.5 0

$B$101 Sales of Set - Steel Insert on Chandler (1st Month) 0 -78 0 53.5 0

$B$102 Sales of Set - Graphite, Metal on Chandler (1st Month) 0 -20 0 53.5 0

$B$103 Sales of Set - Graphite, Insert on Chandler (1st Month) 53.5 0 0 53.5 1E+30

$C$95 Sales of Steel shafts on Glendale (1st Month) 0 0 2000 1E+30 2000

$C$96 Sales of Graphite shafts on Glendale (1st Month) 100 0 2000 1E+30 1900

$C$97 Sales of Forged iron heads on Glendale (1st Month) 200 0 2000 1E+30 1800

$C$98 Sales of Metal Wood heads on Glendale (1st Month) 30 0 2000 1E+30 1970

$C$99 Sales of Titanium Insert heads on Glendale (1st Month) 2000 5.81042654 2000 723 760.8518998

$C$100 Sales of Set - Steel, Metal on Glendale (1st Month) 0 0 200 1E+30 200

$C$101 Sales of Set - Steel Insert on Glendale (1st Month) 0 0 100 1E+30 100

$C$102 Sales of Set - Graphite, Metal on Glendale (1st Month) 0 0 300 1E+30 300

$C$103 Sales of Set - Graphite, Insert on Glendale (1st Month) 34.26540284 0 400 1E+30 365.7345972$C$95 Sales of Steel shafts on Glendale (1st Month) 0 -2.132701422 0 1032.857143 0

$C$96 Sales of Graphite shafts on Glendale (1st Month) 100 -0.132701422 100 824.2562248 100

$C$97 Sales of Forged iron heads on Glendale (1st Month) 200 -6.170616114 200 803.3333333 200

$C$98 Sales of Metal Wood heads on Glendale (1st Month) 30 -2.170616114 30 803.3333333 30

$C$99 Sales of Titanium Insert heads on Glendale (1st Month) 2000 0 100 1900 1E+30

$C$100 Sales of Set - Steel, Metal on Glendale (1st Month) 0 -96.94312796 0 34.75961538 0

$C$101 Sales of Set - Steel Insert on Glendale (1st Month) 0 -55 0 34.26540284 0

$C$102 Sales of Set - Graphite, Metal on Glendale (1st Month) 0 -11.94312796 0 34.75961538 0

$C$103 Sales of Set - Graphite, Insert on Glendale (1st Month) 34.26540284 0 0 34.26540284 1E+30

$D$95 Sales of Steel shafts on Tucson (1st Month) 0 0 2000 1E+30 2000

$D$96 Sales of Graphite shafts on Tucson (1st Month) 2000 0.1937046 2000 403 1950

$D$97 Sales of Forged iron heads on Tucson (1st Month) 100 0 2000 1E+30 1900

$D$98 Sales of Metal Wood heads on Tucson (1st Month) 15 0 2000 1E+30 1985

$D$99 Sales of Titanium Insert heads on Tucson (1st Month) 2000 7.539951574 2000 377.8125 930.7815006


16/18

15

$D$100 Sales of Set - Steel, Metal on Tucson (1st Month) 0 0 200 1E+30 200

$D$101 Sales of Set - Steel Insert on Tucson (1st Month) 0 0 100 1E+30 100

$D$102 Sales of Set - Graphite, Metal on Tucson (1st Month) 0 0 300 1E+30 300

$D$103 Sales of Set - Graphite, Insert on Tucson (1st Month) 14.63680387 0 400 1E+30 385.3631961

$D$95 Sales of Steel shafts on Tucson (1st Month) 0 -4.8062954 0 403 0

$D$96 Sales of Graphite shafts on Tucson (1st Month) 2000 0 50 1950 1E+30

$D$97 Sales of Forged iron heads on Tucson (1st Month) 100 -6.113801453 100 355.5882353 100

$D$98 Sales of Metal Wood heads on Tucson (1st Month) 15 -1.113801453 15 355.5882353 15

$D$99 Sales of Titanium Insert heads on Tucson (1st Month) 2000 0 100 1900 1E+30

$D$100 Sales of Set - Steel, Metal on Tucson (1st Month) 0 -141.9612591 0 14.53125 0

$D$101 Sales of Set - Steel Insert on Tucson (1st Month) 0 -90 0 14.63680387 0

$D$102 Sales of Set - Graphite, Metal on Tucson (1st Month) 0 -1.96125908 0 14.53125 0

$D$103 Sales of Set - Graphite, Insert on Tucson (1st Month) 14.63680387 0 0 14.63680387 1E+30

$R$15 Labor on Chandler (2nd Month) 11027.75 0 12000 1E+30 972.25

$R$16 Packing on Chandler (2nd Month) 20000 1.496666667 20000 2509.032258 6420$R$27 Labor on Glendale (2nd Month) 15000 1.543127962 15000 5176.666667 3615

$R$28 Packing on Glendale (2nd Month) 23148.95735 0 40000 1E+30 16851.04265

$R$38 Labor on Tucson (2nd Month) 20042.03125 0 22000 1E+30 1957.96875

$R$39 Packing on Tucson (2nd Month) 35000 1.084615385 35000 1552.5 17647.5

$M$53 Assembly Time on Chandler (2nd Month) 3477.5 0 5500 1E+30 2022.5

$O$53 Assembly Time on Tucson (2nd Month) 5514.84375 0 6000 1E+30 485.15625

$N$53 Assembly Time on Glendale (2nd Month) 2055.924171 0 5000 1E+30 2944.075829

$L$60 Advertising (2nd Month) 18262.14624 0 20000 1E+30 1737.853762

$M$66 Graphite (in pounds) (2nd Month) 623.4797467 0 1000 1E+30 376.5202533

$M$73 Sales of Steel shafts on Chandler (2nd Month) 0 0 2000 1E+30 2000

$M$74 Sales of Graphite shafts on Chandler (2nd Month) 100 0 2000 1E+30 1900

$M$75 Sales of Forged iron heads on Chandler (2nd Month) 200 0 2000 1E+30 1800

$M$76 Sales of Metal Wood heads on Chandler (2nd Month) 30 0 2000 1E+30 1970

$M$77 Sales of Titanium Insert heads on Chandler (2nd Month) 2000 1.9 2000 580.4477612 622.3076923


17/18

16

$M$78 Sales of Set - Steel, Metal on Chandler (2nd Month) 0 0 200 1E+30 200

$M$79 Sales of Set - Steel Insert on Chandler (2nd Month) 0 0 100 1E+30 100

$M$80 Sales of Set - Graphite, Metal on Chandler (2nd Month) 0 0 300 1E+30 300

$M$81 Sales of Set - Graphite, Insert on Chandler (2nd Month) 53.5 0 400 1E+30 346.5

$M$73 Sales of Steel shafts on Chandler (2nd Month) 0 -2.706666667 0 1605 0

$M$74 Sales of Graphite shafts on Chandler (2nd Month) 100 -2.266666667 100 1605 100

$M$75 Sales of Forged iron heads on Chandler (2nd Month) 200 -3.963333333 200 1284 200

$M$76 Sales of Metal Wood heads on Chandler (2nd Month) 30 -2.18 30 1070 30

$M$77 Sales of Titanium Insert heads on Chandler (2nd Month) 2000 0 100 1900 1E+30

$M$78 Sales of Set - Steel, Metal on Chandler (2nd Month) 0 -88.96 0 53.5 0

$M$79 Sales of Set - Steel Insert on Chandler (2nd Month) 0 -54.96 0 53.5 0

$M$80 Sales of Set - Graphite, Metal on Chandler (2nd Month) 0 -11.6 0 53.5 0

$M$81 Sales of Set - Graphite, Insert on Chandler (2nd Month) 53.5 0 0 53.5 1E+30

$N$73 Sales of Steel shafts on Glendale (2nd Month) 0 0 2000 1E+30 2000

$N$74 Sales of Graphite shafts on Glendale (2nd Month) 100 0 2000 1E+30 1900$N$75 Sales of Forged iron heads on Glendale (2nd Month) 200 0 2000 1E+30 1800

$N$76 Sales of Metal Wood heads on Glendale (2nd Month) 30 0 2000 1E+30 1970

$N$77 Sales of Titanium Insert heads on Glendale (2nd Month) 2000 5.40436019 2000 723 1035.333333

$N$78 Sales of Set - Steel, Metal on Glendale (2nd Month) 0 0 200 1E+30 200

$N$79 Sales of Set - Steel Insert on Glendale (2nd Month) 0 0 100 1E+30 100

$N$80 Sales of Set - Graphite, Metal on Glendale (2nd Month) 0 0 300 1E+30 300

$N$81 Sales of Set - Graphite, Insert on Glendale (2nd Month) 34.26540284 0 400 1E+30 365.7345972

$N$73 Sales of Steel shafts on Glendale (2nd Month) 0 -1.000947867 0 1032.857143 0

$N$74 Sales of Graphite shafts on Glendale (2nd Month) 100 -0.560947867 100 1032.857143 100

$N$75 Sales of Forged iron heads on Glendale (2nd Month) 200 -4.544075829 200 803.3333333 200

$N$76 Sales of Metal Wood heads on Glendale (2nd Month) 30 -1.264075829 30 803.3333333 30

$N$77 Sales of Titanium Insert heads on Glendale (2nd Month) 2000 0 100 1900 1E+30

$N$78 Sales of Set - Steel, Metal on Glendale (2nd Month) 0 -66.48530806 0 34.75961538 0

$N$79 Sales of Set - Steel Insert on Glendale (2nd Month) 0 -29.2 0 34.26540284 0


18/18

17

$N$80 Sales of Set - Graphite, Metal on Glendale (2nd Month) 0 -3.685308057 0 34.75961538 0

$N$81 Sales of Set - Graphite, Insert on Glendale (2nd Month) 34.26540284 0 0 34.26540284 1E+30

$O$73 Sales of Steel shafts on Tucson (2nd Month) 0 0 2000 1E+30 2000

$O$74 Sales of Graphite shafts on Tucson (2nd Month) 50 0 2000 1E+30 1950

$O$75 Sales of Forged iron heads on Tucson (2nd Month) 100 0 2000 1E+30 1900

$O$76 Sales of Metal Wood heads on Tucson (2nd Month) 15 0 2000 1E+30 1985

$O$77 Sales of Titanium Insert heads on Tucson (2nd Month) 2000 6.083076923 2000 1156.981534 194.0625

$O$78 Sales of Set - Steel, Metal on Tucson (2nd Month) 0 0 200 1E+30 200

$O$79 Sales of Set - Steel Insert on Tucson (2nd Month) 0 0 100 1E+30 100

$O$80 Sales of Set - Graphite, Metal on Tucson (2nd Month) 84.84375 0 300 1E+30 215.15625

$O$81 Sales of Set - Graphite, Insert on Tucson (2nd Month) 0 0 400 1E+30 400

$O$73 Sales of Steel shafts on Tucson (2nd Month) 0 -3.974615385 0 2000 0

$O$74 Sales of Graphite shafts on Tucson (2nd Month) 50 -0.534615385 50 1950 50

$O$75 Sales of Forged iron heads on Tucson (2nd Month) 100 -4.819230769 100 1900 100

$O$76 Sales of Metal Wood heads on Tucson (2nd Month) 15 -0.659230769 15 1985 15$O$77 Sales of Titanium Insert heads on Tucson (2nd Month) 2000 0 100 1900 1E+30

$O$78 Sales of Set - Steel, Metal on Tucson (2nd Month) 0 -117.2 0 84.84375 0

$O$79 Sales of Set - Steel Insert on Tucson (2nd Month) 0 -72.77307692 0 85.46004843 0

$O$80 Sales of Set - Graphite, Metal on Tucson (2nd Month) 84.84375 0 0 84.84375 1E+30

$O$81 Sales of Set - Graphite, Insert on Tucson (2nd Month) 0 -7.973076923 0 85.46004843 0

Documents

Industrial Engineering - Operations Research I - Case Study