12 November (1)

Microsoft Excel 14.0 Answer Report

Worksheet: [12 November.xlsx]Animal Feed Company

Report Created: 12-11-2013 19:39:29

Result: Solver found a solution. All Constraints and optimality conditions are satisfied.

Solver Engine

Solver Options

Objective Cell (Min)

Cell Name Original Value Final Value

$B$15 Minimum Cost (Rs) Total 840 840

Variable Cells

Cell Name Original Value Final Value Integer

$C$11 X1 Usage 80 80 Contin


Constraints

Cell Name Cell Value Formula Status Slack

$C$13 Total Usage 200 $C$13=$B$8 Binding 0

$C$12 X2 Usage 120 $C$12>=$B$12 Not Binding 60

$C$11 X1 Usage 80 $C$11<=$B$11 Binding 0

Experiment 1 29 July, 2013

Target (Kg) 200

Resources Limit Usage Rate Cost

X1 80 80 3 240

X2 60 120 5 600

Total 200

Minimum Cost (Rs) 840


Worksheet: [Book1]Animal Feed Company

Report Created: 7/29/2013 12:11:39 PM



$B$15 Minimum Cost (Rs) Total 840 840

Variable Cells




Constraints


$C$13 Total Usage 200 $C$13=$B$8 Binding 0

$C$12 X2 Usage 120 $C$12>=$B$12Not Binding 60

$C$11 X1 Usage 80 $C$11<=$B$11Binding 0

An animal Feed company must produce exactly 200Kg of a mixture consisting of ingridients X1 and X2. The ingridients X1 costs Rs 3/Kg and X2 costs Rs 5/Kg. Not more than 80Kg of X1 can be used and atleast 60Kg of X2 must be used. Find the minimum cost of mixture.

Nikhil Sorout: A50105410093




Worksheet: [Book1]Sheet1

Report Created: 7/29/2013 11:44:23 AM

Target Cell (Max)


$H$33 Profit 0 1360

Adjustable Cells


$B$28 Number of Bowls 0 24

$C$28 Number of Mugs 0 8

Constraints


$G$22 Labour Usage 40 $G$22<=$F$22 Binding 0

$G$23 Clay Usage 120 $G$23<=$F$23 Binding 0


Data Table

Product Bowl Mug

Profit 40 50

Resource List

Resources Bowl Mug Available Used

Labour 1 2 40 40

Clay 4 3 120 120

Number of Bowls Number of Mugs

24 8

Profit: 1360


Worksheet: [Book1]Sheet1

Report Created: 7/29/2013 11:44:23 AM

Target Cell (Max)


$H$33 Profit 0 1360

Adjustable Cells


$B$28 Number of Bowls 0 24

$C$28 Number of Mugs 0 8

Constraints


$G$22 Labour Usage 40 $G$22<=$F$22 Binding 0

$G$23 Clay Usage 120 $G$23<=$F$23 Binding 0

Optimized Production Plan

A company makes bowls and mugs from clay. The profit earned in making cups and bowls is Rs40 & Rs50 repectively. Making a cup requires 1 labour and 4 pounds of clay while making a mug requires 2 albours and 3 pounds of clay. 40 Labour and 120 pounds of clay are available per day. Formulate an LPP to maximize the profit.



Worksheet: [12 November.xlsx]August 5 (I)

Report Created: 12-11-2013 20:22:34


Solver Engine

Solver Options



$B$25 Total Cost (Rs.) Contractor 1 0 4900

Variable Cells


$B$19:$E$22

Constraints


$F$19:$F$22 = 1

$B$23:$E$23 = 1

Experiment 3 5 August, 2013

Bid Matrix

. Contractor 1 Contractor 2 Contractor 3 Contractor 4

Assembly 1 15 13 14 17

Assembly 2 11 12 15 13

Assembly 3 13 12 10 11

Assembly 4 15 17 14 16

. Contractor 1 Contractor 2 Contractor 3 Contractor 4 Row Sum

Assembly 1 0 1 0 0 1




Column Sum 1 1 1 1

Total Cost (Rs.) 4900

Constraints

$B$23:$E$23 = 1

Assignment Matrix

A machine tool company decides to make 4 sub-assemblies through 4 sub-contractors. Each contractor is to receive only 1 sub-assembly. The cost of each sub-assembly is determined by the bids submitted by each contractor and is shown in the table in 100s' of Rs. Assign the assemblies to minimise the cost.


Experiment 3 5 August, 2013


Worksheet: [12 November.xlsx]August 5 (I)

Report Created: 12-11-2013 20:22:34

Solver Engine

Engine: Simplex LP

Solution Time: 0.016 Seconds.

Iterations: 7 Subproblems: 0

Solver Options

Max Time 100 sec, Iterations 100, Precision 0.000001


Cell Name Original ValueFinal Value

$B$25 Total Cost (Rs.) Contractor 1 0 4900

Variable Cells

Cell Name Original ValueFinal Value Integer

$B$19:$E$22

$B$19 Assembly 1 Contractor 1 0 0 Contin

$C$19 Assembly 1 Contractor 2 0 1 Contin

$D$19 Assembly 1 Contractor 3 0 0 Contin

$E$19 Assembly 1 Contractor 4 0 0 Contin













Constraints


$F$19:$F$22 = 1

$F$19 Assembly 1 Row Sum 1 $F$19=1 Binding 0




$B$23:$E$23 = 1


Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5%, Solve

Without Integer Constraints, Assume NonNegative



Worksheet: [12 November.xlsx]Machine Assignment Problem



Solver Engine

Engine: Simplex LP



Solver Options


Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5%, Solve Without Integer Constraints, Assume NonNegative

Objective Cell (Max)


$C$27 Total Profit Job 2 50 50

Variable Cells


$B$19 Machine 1 Job 1 0 0 Contin

$C$19 Machine 1 Job 2 0 0 Contin

$D$19 Machine 1 Job 3 1 1 Contin

$E$19 Machine 1 Job 4 0 0 Contin

$F$19 Machine 1 Job 5 0 0 Contin





















Constraints


$G$19 Machine 1 Row Sum 1 $G$19=1 Binding 0





$B$24 Column Sum Job 1 1 $B$24=1 Binding 0

$C$24 Column Sum Job 2 1 $C$24=1 Binding 0

$D$24 Column Sum Job 3 1 $D$24=1 Binding 0

$E$24 Column Sum Job 4 1 $E$24=1 Binding 0

$F$24 Column Sum Job 5 1 $F$24=1 Binding 0

Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5%, Solve Without Integer Constraints, Assume NonNegative

Experiment 4

Profit Matrix

. Job 1 Job 2 Job 3 Job 4 Job 5

Machine 1 5 11 10 12 4

Machine 2 2 4 6 3 5

Machine 3 3 12 5 14 6

Machine 4 6 14 4 11 7

Machine 5 7 9 8 12 5

. Job 1 Job 2 Job 3 Job 4 Job 5 Row Sum

Machine 1 0 0 1 0 0 1

Machine 2 0 0 0 0 1 1

Machine 3 0 0 0 1 0 1

Machine 4 0 1 0 0 0 1

Machine 5 1 0 0 0 0 1

Column Sum 1 1 1 1 1

Total Profit 50


Worksheet: [12 November.xlsx]Machine Assignment Problem



Solver Engine

Engine: Simplex LP



Solver Options




$C$27 Total Profit Job 2 50 50

Assignment Matrix

Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5%, Solve

Without Integer Constraints, Assume NonNegative

A company has 5 jobs to be done. The following matrix shows the return in rupees of assigning Ith machine to Jth job. Assign the 5 Jobs to 5 machines so as to maximize the total expected profit.


Experiment 4

Variable Cells



























Constraints







$B$24 Column Sum Job 1 1 $B$24=1 Binding 0

$C$24 Column Sum Job 2 1 $C$24=1 Binding 0

$D$24 Column Sum Job 3 1 $D$24=1 Binding 0

$E$24 Column Sum Job 4 1 $E$24=1 Binding 0

$F$24 Column Sum Job 5 1 $F$24=1 Binding 0


Experiment 4

machine



Worksheet: [12 November.xlsx]Cooler



Solver Engine

Engine: Simplex LP



Solver Options

Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling

Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative



$B$28 Net Profit Ranchi 0 31600

Variable Cells


$B$24 Mumbai Ranchi 0 75 Contin

$C$24 Mumbai Delhi 0 95 Contin

$D$24 Mumbai Lucknow 0 0 Contin

$E$24 Mumbai Kanpur 0 30 Contin

$B$25 Kolkata Ranchi 0 0 Contin

$C$25 Kolkata Delhi 0 0 Contin

$D$25 Kolkata Lucknow 0 100 Contin

$E$25 Kolkata Kanpur 0 0 Contin

Constraints


$B$26 Demand Met Ranchi 75 $B$26<=$B$15 Binding 0

$C$26 Demand Met Delhi 95 $C$26<=$C$15 Not Binding 5

$D$26 Demand Met Lucknow 100 $D$26<=$D$15 Binding 0

$E$26 Demand Met Kanpur 30 $E$26<=$E$15 Binding 0

$F$24 Mumbai Optimized Production Rate 200 $F$24<=$B$19 Binding 0

$F$25 Kolkata Optimized Production Rate 100 $F$25<=$B$20 Binding 0

Experiment 6

Profit Matrix

. Ranchi Delhi Lucknow Kanpur

Mumbai 90 90 100 110

Kolkata 50 70 130 85

. Ranchi Delhi Lucknow Kanpur

Demand 75 100 100 30

Plant Capacity

Mumbai 200

Kolkata 100

. Ranchi Delhi Lucknow Kanpur Optimized Production Rate

Mumbai 75 95 0 30 200

Kolkata 0 0 100 0 100

Demand Met 75 95 100 30

Net Profit 31600

$B$26

$C$26

$D$26

$E$26

$F$24

$F$25

Demand Matrix

Production Allotment

Capacity Chart

A company manufacturing air collers has 2 plants located at Mumbai and Kolkata with a capacity of 200 & 100 units per week. The company has to supply the coolers to its' 4 showrooms located at Ranchi, Delhi, Lucknow and Kanpur which have a maximum demand of 75; 100; 100 & 30 units respectively. Due to variations in material and transportation cost the profit per unit differs and is given in the table. Plan the production in order to maximize the profit. The plants can be run undercapacity.


Experiment 6


Worksheet: [12 November.xlsx]Cooler



Solver Engine

Engine: Simplex LP



Solver Options

Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling



$B$28 Net Profit Ranchi 0 31600

Variable Cells

Cell Name Original ValueFinal Value Integer

$B$24 Mumbai Ranchi 0 75 Contin

$C$24 Mumbai Delhi 0 95 Contin

$D$24 Mumbai Lucknow 0 0 Contin

$E$24 Mumbai Kanpur 0 30 Contin

$B$25 Kolkata Ranchi 0 0 Contin

$C$25 Kolkata Delhi 0 0 Contin

$D$25 Kolkata Lucknow 0 100 Contin

$E$25 Kolkata Kanpur 0 0 Contin

Constraints


$B$26 Demand Met Ranchi 75 $B$26<=$B$15Binding 0

$C$26 Demand Met Delhi 95 $C$26<=$C$15Not Binding 5

$D$26 Demand Met Lucknow 100 $D$26<=$D$15Binding 0

$E$26 Demand Met Kanpur 30 $E$26<=$E$15Binding 0

$F$24 Mumbai Optimized Production Rate 200 $F$24<=$B$19Binding 0

$F$25 Kolkata Optimized Production Rate 100 $F$25<=$B$20Binding 0

Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume Non-

Negative

company manufacturing air collers has 2 plants located at Mumbai and Kolkata with a capacity of 200 & 100



Worksheet: [12 November.xlsx]Car Rental


Target Cell (Min)


$B$27 Total Cost 1 185 185

Adjustable Cells


$B$19 1 0 0

$C$19 2 0 0

$D$19 3 0 0

$E$19 4 0 0

$F$19 5 1 1

$G$19 6 0 0

$B$20 1 0 0

$C$20 2 1 1

$D$20 3 0 0

$E$20 4 0 0

$F$20 5 0 0

$G$20 6 0 0

$B$21 1 1 1

$C$21 2 0 0

$D$21 3 0 0

$E$21 4 0 0

$F$21 5 0 0

$G$21 6 0 0

$B$22 1 0 0

$C$22 2 0 0

$D$22 3 1 1

$E$22 4 0 0

$F$22 5 0 0

$G$22 6 0 0

$B$23 1 0 0

$C$23 2 0 0

$D$23 3 0 0

$E$23 4 1 1

$F$23 5 0 0

$G$23 6 0 0

$B$24 1 0 0

$C$24 2 0 0

$D$24 3 0 0

$E$24 4 0 0

$F$24 5 0 0

$G$24 6 1 1

Constraints


$H$19 Row Sum 1 $H$19=1 Not Binding 0






$B$25 Column Sum 1 1 $B$25=1 Not Binding 0

$C$25 Column Sum 2 1 $C$25=1 Not Binding 0

$D$25 Column Sum 3 1 $D$25=1 Not Binding 0

$E$25 Column Sum 4 1 $E$25=1 Not Binding 0

$F$25 Column Sum 5 1 $F$25=1 Not Binding 0

$G$25 Column Sum 6 1 $G$25=1 Not Binding 0

Transportation cost chart

Cities 1 2 3 4 5 6

7 41 72 39 52 25 51

8 22 29 49 65 81 50

9 27 39 60 51 32 32

10 45 50 48 52 37 43

11 29 40 39 26 30 33

12 32 40 40 60 51 30

Cities 1 2 3 4 5 6 Row Sum

7 0 0 0 0 1 0 1

8 0 1 0 0 0 0 1

9 1 0 0 0 0 0 1

10 0 0 1 0 0 0 1

11 0 0 0 1 0 0 1

12 0 0 0 0 0 1 1

Column Sum 1 1 1 1 1 1

Total Cost 185


Worksheet: [12 November.xlsx]Car Rental


Target Cell (Min)


$B$27 Total Cost 1 185 185

Adjustable Cells


$B$19 1 0 0

$C$19 2 0 0

$D$19 3 0 0

$E$19 4 0 0

$F$19 5 1 1

$G$19 6 0 0

$B$20 1 0 0

Assignment Matrix

A national car rental service has surplus of cars in cities (1-6) and a deficiency of 1 car in cities (7-12). The distance between the two cities is given below. Assign the travel route so as to minimize the transportation cost.


$C$20 2 1 1

$D$20 3 0 0

$E$20 4 0 0

$F$20 5 0 0

$G$20 6 0 0

$B$21 1 1 1

$C$21 2 0 0

$D$21 3 0 0

$E$21 4 0 0

$F$21 5 0 0

$G$21 6 0 0

$B$22 1 0 0

$C$22 2 0 0

$D$22 3 1 1

$E$22 4 0 0

$F$22 5 0 0

$G$22 6 0 0

$B$23 1 0 0

$C$23 2 0 0

$D$23 3 0 0

$E$23 4 1 1

$F$23 5 0 0

$G$23 6 0 0

$B$24 1 0 0

$C$24 2 0 0

$D$24 3 0 0

$E$24 4 0 0

$F$24 5 0 0

$G$24 6 1 1

Constraints








$B$25 Column Sum 1 1 $B$25=1 Not Binding 0

$C$25 Column Sum 2 1 $C$25=1 Not Binding 0

$D$25 Column Sum 3 1 $D$25=1 Not Binding 0

$E$25 Column Sum 4 1 $E$25=1 Not Binding 0

$F$25 Column Sum 5 1 $F$25=1 Not Binding 0

$G$25 Column Sum 6 1 $G$25=1 Not Binding 0



Not a part of practical file

Machine Product 1 Product 2 Product 3Machine

Capacity

Total minutes

utilized

M1 2 3 2 440 440

M2 4 0 3 470 470

M3 2 5 0 430 211.1111111

Profit/Unit

(Rs)4 3 6

Product P1 P2 P3

Number 0 42.2222222 156.666667

Profit 0 126.666667 940

Total Profit 1066.66667

Time/Unit (minutes)

A firm produces 3 Products which are being processed on 3 different machines. The time required to manufacture 1 unit of each of the 3 products and the daily capacity of the 3 machines are given in the table. It is required to determine the daily no of units to be manufactured for each product. The profit per unit for products are Rs 4,3,6 respectively. It's assumed that all the amounts produced are consumed in the market. Formulate L.P.P to maximize the daily profit and solve it using in-built solver.


Not a part of practical file


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12 November (1)