Formulate but do not solve the following exercise as a linear programming problem. A farmer uses two types of fertilizers. A 50-1b bag of Fertilizer A contains 8 lb of nitrogen, 2 lb of phosphorus, and 4 lb of potassium. A 50-lb bag of Fertilizer B contains 5 lb each of nitrogen, phosphorus, and potassium. The minimum requirements for a field are 440 lb of nitrogen, 260 lb of phosphorus, and 360 lb of potassium. If a 50-1b bag of Fertilizer A costs $50 and a 50-1b bag of Fertilizer B costs $30, find the amount of each type of fertilizer the farmer should use to minimize his cost C in dollars while still meeting the minimum requirements. (Let x represent the number of bags of Fertilizer A and y represent the number of bags of Fertilizer B.) Minimize C = X subject to the constraints nitrogen phosphorus potassium X>0 y20