Machinco produces four products, requiring time on two machines and two types (skilled and unskilled) of labor. The amount of machine time and labor (in hours) used by each product and the sales prices are given in Table.
|
Product
|
Machine 1
|
Machine 2
|
Skilled
|
Unskilled
|
Sales ($)
|
|
1
|
11
|
4
|
8
|
7
|
300
|
|
2
|
7
|
6
|
5
|
8
|
260
|
|
3
|
6
|
5
|
4
|
7
|
220
|
|
4
|
5
|
4
|
6
|
4
|
180
|
Each month, 700 hours are available on machine 1 and 500 hours on machine 2. Each month, Machinco can purchase up to 600 hours of skilled labor at $8 per hour and up to 650 hours of unskilled labor at $6 per hour. Formulate an LP that will enable Machinco to maximize its monthly profit. Solve this LP and use the output to answer the following questions:
a By how much does the price of product 3 have to increase before it becomes optimal to produce it?
b If product 1 sold for $290, then what would be the new optimal solution to the problem?
c What is the most Machinco would be willing to pay for an extra hour of time on each machine?
d What is the most Machinco would be willing to pay for an extra hour of each type of labor?
e If up to 700 hours of skilled labor could be purchased each month, then what would be Machinco's monthly profits?