please answer a through e

Your company produces three products, Model Alpha, Model Beta and Model Delta. The contribution of the products is 4400 (for Alpha), S6000 (for Beta) and S3200 (for Delta). If your company stay in business (.e. if it produces any products), then it must absorb a fixed cost of S200,000. 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, 6 Process 1 Process 2 Process 3 Model Alpha Model Beta Model Delta Time Available 14 12 480 5 260 15 30 1200 6 10 (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 $200,000) Alpha Beta- Delta Contribution- Profit (c) If you could buy extra capacity of Process I, 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) 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 Model Gamma 12 Contribution from Gamma would need to be_ (e) Go back and look at question (b). If the Fixed Cost was $300,000, what would be your answe SWETS to (b)? Delta- Alpha Contribution- Beta- Profit