Optimal Product Mix- Linear Programming

Your company produces three products, Model Alpha, Model Beta and Model Delta. The contribution of the products is $2200 (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.

(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? (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" program to the original program written in (a).