The American Metal Fabrication Company(AMFC) produces various products from steel bars. One of theinitial steps is a shaping operation, which is performed by rollingmachines. There are three machines available for this purpose, theB3, B4, and B5. There features are given by the followingtable:
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. AMFCmust produce at least 218,000 feet of ¼ in. material, 114,000 feetof 3/8 in. material, and 111,000 feet of ½ in. material. The profitcontribution per foot excluding labor for these products are .017,.019 and .02. These prices apply to all production, e.g., any inexcess of the required production. The shipping department has acapacity limit of 600,000 feet per week, regardless of thethickness. Formulate a linear programming model to maximizeprofit.
      a)   Please define your variables clearly and theunits used.
      b)  What is the value of an additional hour of capacityon the B4 machine?
      c)   What is the value of an additional 2 hours ofcapacity on the B3 machine?
      d)  By how much would one have to raise the profitcontribution/1,000 ft. of ¼†material before it would be worthproducing more of it?
