PROBLEM 1 Optimization (50 points) A local farmer, Jerry Glover, operates a 1200-acre irrigated farm in rural Water District No. 6. District Authority has just given its water allotments for the next year (Jerry was allotted 2000 acre-feet) and Jer is busy preparing his production plan for next year. His problem is that of deciding what to grow; alfalfa corn or soy beans or a combination of those. One ton of alfalfa takes 0.35 acres of land, 0.75 acre/ft of water and will bring an expected profit of $24. One ton of corn takes 0.2 acres of land, 0.90 acre/ft of water and nets $20. One ton of soy beans takes 0.3 acres of land, 0.8 acre/ft of water and nets $28 Formulate Jerry's production problem as the linear programming optimization problem Answer the following questions and DEFEND YOUR ANSWERS alfaalfa corn Soy and water nets 0.35 0.75 0.2 0.9 0.3 0.8 $24.00 $20.00 $28.00 a) What is the best solution for Jerry? How much is his profit? b) If the profit of corn increase to $30 per ton will Jerry produce any corn? Is the overall profit going to change? Explain c) If only 1000 acres of land was available would his profit remain the same? Explain d) Jerry has option of increasing his allotted 2000 acre-feet to 2200 acre-feet at a price of $33 per acre-feet. Is this profitable? Explain