SOLVE BY SENSITIVITY-ADD VARIABLE

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OPTIMIZATION METHODS Exercise 1.- Farmer Jane owns 45 acres of land. She is going to plant each with wheat or corn. Each acre planted with wheat yields $200 profit; each with corn yields $300 profit. The labour and fertilizer used for each acre are given in the table below. One hundred workers and 120 tons of fertilizer are available. Use linear programming to determine how Jane maximizes profits from her land. Wheat 3 workers 2 tons Corn 2 workers Labour Fertilizer 4 tons W C $1 S2 S3 RHS Ratio S1 1 1 1 0 0 45 45 3 2 0 1 0 S2 S3 100 120 50 30 4 0 0 1 2 200 Z 300 0 0 0 0 W C 51 S2 S3 Ratio RHS 15 S1 0.5 0 1 0 -0.25 37.5 35 S2 2 0 0 1 -0.5 40 1 0 0 0.25 30 7.5 0.5 50 Z 0 0 0 -75 -9000 W S1 S2 S3 RHS S1 0 0 1 -0.25 -0.125 W 1 0 0 0.5 5 20 20 0 1 0 -0.25 0.375 -62.5 -0.25 Z 0 0 0 -25 -10000 a) Find the new optimal solution with a another product Labour Fertilizer Price New Product 3 workers 3 tons 200 b) Find the new optimal solution if the price is 350 W C X3 51 S2 S3 RHS Ratio WC X3 S1 S2 S3 RHS Ratio W= C= X3=