Reference no: EM13578751
Your company produces two products, Model Alpha and Model Beta. These products have profits (or contributions) of $120 and $180 respectively.
Each model is produced in a four 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
|
Total Time Available
|
|
Process 1
|
10
|
20
|
300
|
|
Process 2
|
6
|
3
|
72
|
|
Process 3
|
5
|
3
|
100
|
|
Process 4
|
20
|
30
|
600
|
|
|
|
|
(a) You are asked to select the combination of Model Alpha and Model Beta that will maximize the profitability of your company. Write the linear program that solves this problem in the space below.
(b) Using a ruler and/or graph paper, sketch the set that shows the combinations of Model Alpha and Model Beta that can be produced. (attach to exam)
(c) Using ruler and/or graph paper, make a separatesketch that shows a family of "contour lines" that show various combinations of Model Alpha and Model Beta that will produce profit of $1200 and $1800 respectively. (attach to exam)
(d) Find the combination of Model Alpha and Model Beta that maximizes the firm profit. What is firm's profit at this profit mix?
Alpha = ______Beta = __________ Profit = ______________
(e) If you could buy extra capacity of Process 4, 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 = _______________
(f) Write the "dual" program to the original program written in (a).
(g) 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?
|
Gamma
|
|
Process 1
|
8
|
|
Process 2
|
6
|
|
Process 3
|
4
|
|
Process 4
|
26
|
|
|
|
Contribution from Gamma would need to be _____________________________.