Formulate but do not solve the following exercise as a linea

Formulate but do not solve the following exercise as a linear programming problem. A farmer uses two types of fertilizers. A 50-lb 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-lb bag of Fertilizer A costs $80 and a 50-lb bag of Fertilizer B costs $40, 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 = subject to the constraints nitrogen phosphorus potassium x 0 y 0

Solution

the minimum cost of meeting all the requirements is $1720 when the farmer buy 20 bags ofA and 56 bags of B