A fertilizer manufacturer produces two types of fertilizer - Regular and Green-Up. Regular should have at least 14 percent nitrogen and 20 percent phosphorous. Green-Up should have at least 15 percent nitrogen and 22 percent phosphorous. Each of these products is made by using two components – component A and component B. Component A costs $0.30 per pound and is 12 percent nitrogen and 18 percent phosphorous. Component B costs $0.34 per pound and is 18 percent nitrogen and 24 percent phosphorous. The demand for Regular is projected to be 1,200 pounds, and the demand for Green-Up is 24000 pounds. The company will produce exactly the amount of each fertilizer to meet these projected demands. The company wishes to determine how many pounds of Component A and Component B to use in producing Regular fertilizer and how many pounds of Component A and Component B to use in producing Green-Up fertilizer at the least possible cost. A linear program should be used for this.

a. Carefully define the variables that would be used in a linear program.

b. Set up the linear program for this situation to minimize total cost.

c. Solve this linear program.

Answer Sheet:

2. Carefully define the variables that would be used in a linear program.

b. Write the linear program for this situation to minimize total cost.

c. Solve this linear program.

Minimum possible total cost =

Number of pounds of Component A used in Regular =

Number of pounds of Component B used in Regular =

Number of pounds of Component A used in Green-Up =

Number of pounds of Component B used in Green-Up =