The American Metal Fabrication Company (AMFC) produces various products from steel bars. One of the initial steps is a shaping operation, which is performed by rolling machines. There are three machines available for this purpose, the B3, B4, and B5. There features are given by the following table:

Machine	Speed in Feet/Min.	Allowable Raw Material Thickness in Inches	Available Hours Per Week	Labor Cost Per Hour Operating
B3	150	3/16 to 3/8	35	$10
B4	100	5/16 to 1/2	35	$15
B5	75	3/8 to 3/4	35	$17

This week there are three products, which must be processed. AMFC must produce at least 218,000 feet of ¼ in. material, 114,000 feet of 3/8 in. material, and 111,000 feet of ½ in. material. The profit contribution per foot excluding labor for these products are .017, .019 and .02. These prices apply to all production, e.g., any in excess of the required production. The shipping department has a capacity limit of 600,000 feet per week, regardless of the thickness. Formulate a linear programming model to maximize profit.

a) Please define your variables clearly and the units used.

b) What is the value of an additional hour of capacity on the B4 machine?

c) What is the value of an additional 2 hours of capacity on the B3 machine?

d) By how much would one have to raise the profit contribution/1,000 ft. of ¼” material before it would be worth producing more of it?