Why do the company president and sales manager feel that 101s

are making a loss and hence 101s production should be stopped?

From Table B, it costs $40,205 to produce a 101-truck while it sells for

$39,000.

Why do the president and the production manager feel outsourcing

engine assembly will help? No slack in engine assembly currently.

Show Resource Usage worksheet of merton facts.xls.

Why does the controller feel that cutting back on 102s is an answer?

Overheads are the answer and they are dealt next.

1.3 Understanding the Exhibits: 15 minutes

The numbers in Table A are straight forward resource utilization num-

bers. The numbers in Table B show total costs including fixed overheads

allocated based on Table C. Allocation of fixed costs are done based on

the ratio of resource usage. The fallacy in allocating fixed costs based on

product mix to decide the product mix can be illustrated by using the Ex-

hibits worksheet of merton facts.xls. The grayed out areas represent data

that does not change with product mix. Try the following combinations as

a basis for the controllers comments:

(1000, 1500) for negative contributions of 101s and to explain current

exhibit values in Table B,

(2500, 500) for both positive contributions,

(2500, 125) for negative contributions of 102s and

(500, 125) for both negative contributions.

1.4 Relevance of Overheads: 5 minutes

Allocated fixed costs should not be included in deciding the contributions.

The actual costs for (101s, 102s) are:

direct materials - ($24,000, $20,000) from Table B,

direct labor - ($4,000, $4,500) from Table B and,

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variable overhead - ($8,000, $8,500) from Table C.

What are the contributions of 101s and 102s? ($3000, $5000).

1.5 Evaluate current plan: 15 minutes

We use the Evaluate worksheet of merton facts.xls to set up the model

close to the algebraic formulation discussed next.

Analyzing the president and sales managers decision to stop 101s is

easy. The constraints imply that the number of 102s produced should be

given by min[4000/2, 6000/2, 4500/3]. This gives $7.5 million, worse than

the current plan contributions of $10.5 million.

Current plan for productions is (101s, 102s) = (1000, 1500). Is this the

best?

Reduce one model 102 and see how many extra 101s can be produced.

Reducing one 102 frees (2, 2, -, 3) resources in (engine assembly, metals

stamping, 101-assembly, 102-assembly) that can be used to produce two

101s. Show that this increases contribution by $1000 (2 $3000 $5000).

How long can you do this? Net resource effect of the substitution of

each 102 is (-, +2, +4, -3) on remaining resources (-, 1000, 3000, -). This

implies that we can change up to a minimum of (-, 1000/2, 3000/4, -) and

non-negativity requirement on number of 102s produced. Explain that it

is tedious to do this kind of analysis, and more than two product-lines

implies many trade-offs.

1.6 Algebraic Model: 5 minutes

How do we describe the model algebraically? Decisions are coded using

variables called decision variables. How do we express the objective and

constraints using these variables?

Decisions variables:

t101 = number of model 101 trucks produced,

t102 = number of model 102 trucks produced.

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The algebraic formulation is:

max 3000t101 + 5000t102 Objective: contributions,

1t101 + 2t102 4000 Engine Assembly,

2t101 + 2t102 6000 Metal Stamping,

2t101 5000 101 Assembly,

3t102 4500 102 Assembly,

t101 0 Non-negativity,

t102 0 Non-negativity.

1.7 Develop graphical model: 10 minutes

Show merton trucks.ppt, slides 2 through 13. We show how the trade off

that we talked about in section 1.5 moves along the engine assembly ca-

pacity constraint line. In our first 70minute session in 4 sections of roughly

75 students each, we reached this point.

1.8 Develop spreadsheet model: 10 minutes

Excel formulation. Set it up on-line using the Evaluate worksheet of

merton facts.xls.

1.9 Solutions to Problems: 60 minutes

We ask the students to ignore problem 3(b) since it requires reduced costs.

Problem 1: (10 minutes)

a. Optimal monthly mix is (2000, 1000) with a contribution of $11 mil-

lion. This part is already handled while setting up the spreadsheet

optimization model in section 1.8.

b. What is it worth to add an extra hour of engine assembly capacity?

Unutilized resources (engine assembly, metal stamping, 101 assembly,

102 assembly) = (0, 0, 1000, 1500). To use the extra engine assembly

hour, we can give up a 101 truck and make a 102 truck and the net

increase in contribution for the swap (-1, +1) is $2,000. Net effect on

resources is (+1, 0, -2, +3) for the swap. The effect on a graph can be

seen in slides 12 and 13 of merton trucks.ppt.

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c. Resolve to verify that change of engine assembly capacity from 4000 to

4100 hours increases contribution by 2, 000 100 = 0.2million.

d. The number of swaps that we can do is 500.

min

[, , 2000,

1500

3,

]= 500.

Note 101 assembly does not impose a constraint on the number of

swaps directly because each swap increases the unused resources by

two units. But, the number of swaps is constrained by the number

of 101s being produced currently, i.e., 2000. We can not give up more

resources than what we are using.

Problem 2: (10 minutes) This problem should not take much time but

students get confused with the unfortunate wording used in the case. Pro-

duction manager is talking about reimbursing the outside supplier for ma-

terials, labor and overhead. Hence the students question why are we not

considering the fixed overheads in column two of Table C when comput-

ing the results? Fixed overheads are based on Mertons infrastructure and

do not hold for the outside supplier. Only the variable overheads are rele-

vant here.

The second doubt that arises in some students, due to a mis-reading

of the case text, is about what is being outsourced. They assume that a

specific models capacity is increased by the outsourcing. The text is clear

that we do not outsource any specific models engine capacity. Either 101s

or 102s are expected to be made by the outside supplier.

Since we are not using duality, the answer is same as in problem 1 (b)

and 1 (d). Sourcing out engine assembly is acceptable from 1 (b), and the

largest rent Merton can pay is $2000 and no more than 500 hours of engine

assembly can be purchased.

Problem 3: (10 minutes)Model 103:

a. Resources required for 103 = (.8, 1.5, 1, -) and net contribution of $2000.

Re-solve the problem and it is not worth producing. The optimal mix

does not include model 103s and hence no change in contributions.

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