Problem: The Kalo Fertilizer Company produces two brands of lawn fertilizer Super Two and Green Grow – at plants in Fresno, California, and Dearborn, Michigan. The plant at Fresno has resources available to produce 5'000 pounds of fertilizer daily; the plant in Dearborn has enough resources to produce 6'000 pounds daily. The costs – not the profit –per pound of producing each brand is as follows:
|
|
Plant
|
|
Product
|
Fresno
|
Dearborn
|
|
Super Two
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$2
|
$4
|
|
Green Grow
|
$2
|
$3
|
The selling is 9 $/lb for Super Two and 7 $/lb for Green Grow. The company has a daily budget of $45'000 for both plants. Based on past sales, the company knows the maximum demand (converted to a daily basis) is 6'000 pounds for Super Two and 7'000 pounds for Green Grow.. The company wants to know the number of pounds of each brand of fertilizer to produce at each plant in order to maximize profits.
Justify your answers to questions b & c using Sensitivity Analysis
a. Formulate the Linear Programming model for this problem.
b. Management is considering increasing the Fresno production capability by 500 pounds. How would this affect Kalo's profit? Why?
c. Management must reduce its daily budget to $40'000.How will this change affect its profits Why?