Part I. (Optimal Product Mix

Your company produces three products, Model Alpha, Model Beta and Model Delta. The contribution of the products is $2500 (for Alpha), $3000 (for Beta) and $1600 (for Delta).

If your company stay in business (i.e. if it produces any products), then it must absorb a fixed cost of

$100,000.

Each model is produced through a three-process technology. The amount of time used by each model

in each process is outlined below. The total amount of time available to produce all models is also

listed. Using this data, answer the following questions.

	MODEL ALPHA	MODEL BETA	MODEL DELTA	TIME AVAILABLE
PROCESS 1	20	24	12	960
PROCESS 2	28	24	16	1040
PROCESS 3	10	15	30	1200

(a) You are asked to select the combination of Model Alpha, Beta and Delta that will maximize the

profitability of your company. Write the linear program that solves this problem in the space

below.

(b) Find the combination of Model Alpha, Beta & Delta that maximizes the firm contribution and

profit. What is firm's CONTRIBUTION and PROFIT at this profit mix? (hint: remember the

Fixed Cost is $100,000)

Alpha = _____________

Beta = ____________

Delta = ____________

Contribution =____________

Profit = _________________

(c) If you could buy extra capacity of Process 1, what is the most that you would be willing to pay to

purchase it? How many units of capacity would you buy? Be sure to show your work or provide

an appropriate explanation.

Most I would be willing to pay = ____________________________

How many units I would buy = _____________________________?

(d) Write the "dual" programto the original program written in (a).

(e) Suppose that your firm had the ability to produce a new product (Model Gamma). Assume that

this new model used the amount of time for each process listed below. If that is the case, what

would the contribution need to be in order for your firm to produce any units of Model Gamma?

SHOW YOUR WORK - and you must use shadow prices (not "reduced cost").

Contribution from Gamma would need to be ._______________________________

(f) Go back and look at question (b). If the Fixed Cost was $200,000, what would be your answers

to (b)?

Alpha = ____________

Beta = ________________

Delta = ______________

Contribution =____________________

Profit =_______________________