Machino produces four products, which requires time on two machines and two types of labor (skilled and unskilled). The amount of machine time and labor (in hours) used by each product and the sales prices are given in Table . Each month, 700 hours are available on machine 1 and 500 hours on machine 2. Each month, Machino 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 allows Machino to maximize his monthly profit. 

Product	Machine 1	Machine 2	Expert	not trained	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

Solve this LP (using CUTE) and use the result to answer the following questions:

a) How much does the price of product 3 have to increase before it is optimal to produce it?

b) If product 1 sold for $290, what would be the new optimal solution to the problem?

c) What is the most Machino would be willing to pay for an extra hour of time on each machine?

d) What is the most that Machino would be willing to pay for an extra hour of each type of work?

e) If up to 700 hours of skilled labor could be purchased each month, what would Machino's monthly profit be?