A fertilizer manufacturer produces two types of fertilizer - Regular and Green-U
ID: 360803 • Letter: A
Question
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 =
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 =
Explanation / Answer
Answer--
Decision Variables: AR, BR, AG, BG represent th quantity of component A and B used in Regular and Green-up fertilizer respectively
Objective Function: Minimize 0.3AR+0.34BR+0.3AG+0.34BG
s.t. Constraints:
0.12AR+0.18BR 0.14(AR+BR)
0.18AR+0.24BR 0.20(AR+BR)
0.12AG+0.18BG 0.14(AG+BG)
0.18AG+0.24BG 0.20(AG+BG)
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