### COMP 567B           Integer Programming        Assignment 3

#### Due: March 26,  2007   (give to Conor (MC232) by 5pm)

`Consider a farmer who has 500 acres and has to decide how muchland to devote to each of the three crops: wheat, corn and sugar beets. Heknows that he needs 200T of wheat and 240T of corn to feed his cattle.These amounts can be raised or purchased. Any production in excess can besold at a price 170\$/T for wheat and 150\$/T for corn. The purchase priceis 40% higher than the selling price. The farmer can sell sugar beet at aprice 36\$/T. However, for sugar beet that is in excess of the quota he canonly sell for 10\$/T. His quota is 6000. The planting cost is 150\$, 230\$and 260\$ per acre for wheat, corn and sugar beets respectively. Onaverage, the per acre yields are 2.5T, 3T and 20T for wheat, corn and sugar beets.With probability 30%, it will be a good weather next year, which means allyields are 120% of the normal ones and the selling/purchasing price ofwheat/corn is 90% of the normal ones. With probability 30%, it will be bad weather, which means a 80% yield for all crops, and 110% of theselling/purchasing price of wheat/corn. With 40% of probability, theweather is normal and all coefficients are equal to those given above. (Note that the price for sugar beet remains the same for all three scenarios)Formulate this problem into a stochastic linear problem, in both extensiveform and concise form.Solve the LP using CPLEX.`