Three types of fertilizer are manufactured by a company - Regular, Supergro, and Jungle Feeder. Regular should have at least 15 percent nitrogen and 16 percent phosphorous. Supergro should have at least 15 percent nitrogen and 18 percent phosphorous, and Jungle Feeder should have at least 16 percent nitrogen and 20 percent phosphorous. These are made by using two components – Component A and Component B. Component A costs $0.30 per pound and is 14 percent nitrogen and 18 percent phosphorous. Component B costs $0.50 per pound and is 20 percent nitrogen and 24 percent phosphorous. The demand for Regular is projected to be 1,500 pounds, while each of the others has a demand of 3,000 pounds
a) Carefully define the variables that would be used in a linear program.
b) Formulate the linear program for this situation to minimize total cost.