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1. A farmer owns a 100-acre farm and plans to plant at most three crops. The seed for crops A, B, and C costs $40, $20, and $30 per acre, respectively. A maximum of $3,200 can be spent on seed. Crops A, B, and C require 1, 2, and 1 work days per acre, respectively, and there is a maximum of 160 work days available. If the farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B, and $200 per acre on crop C, how many acres of each crop should be planted to maximize profit? What is the maximum profit? X; = number of acres of crop A, X; = number of acres of crop B, *3 =number of acres of crop C. Maximize: P =100x; +300x2 + 200X, Subject to *1 + x2 + x3 $100 40x; + 20x, + 30x, 53200 X; + 2x2 + x, 5160 13 S; S 0 1 1 1 1 0 40 20 30 0 1 0 1 2 1 0 100 0 3.200 0 160 1 0 0 0 1 -100 -300 -200 0 0 0 After several pivots, the following matrix is arrived at. 40 1 0 1 2 0 -1 10 1 OOO 10 0 0 40 -1 800 60 0 1 0 0 1 100 0 100 0 100 0 126,000 Write the answers to the questions: # of acres of crop A - # of acres of crop B- Maximum profit # of acres of crop C = Ont 2. Use the Simplex Method to solve the following linear programmin Maximize: P = 2x, + 2x, Subject to x + x2 36 2x1 + x2 58 4 17,1,20