he Director of physical facilities , is planning to put fertilizer on the grass on campus. The grass needs at least the following amounts of minerals; 30 lbs of nitrogen, 25 lbs of phosphorus and 40 lbs of potash. Two kinds of commercial fertilizers named A and B are available; (analysis and price are given below). The director stores the fertilizers before mixing them together, and he has space for only 300 lbs of fertilizer. Also, he has only $1500 allocated for fertilizers in his budget. Formulate a linear programming model that will determine the optimal quantity (pounds) of each fertilizer he should buy to satisfy his conditions and minimize overall cost.
Fertilizer Characteristics (per lb of fertilizer)
Nitrogen Phosphorus Potash
FertilizerContent(lb) Content(lb) Content(lb)Price
A .22 .14 .36 $ 10
B .16 .55 .15 $8