The Kalo Fertilizer Company produces two brands of lawn fertilizer - Super Two and Green Grow - at plans in Fresno, California, and Dearborn, Michigan. The plan at Fresno has resources available to produce 5,000 pounds of fertilizer daily; the plant at Dearborn has enough resources to produce 6,000 pounds daily. The cost per pound of producing each brand at each plant is as follows.
Product Fresno Dearborn
Super Two $2 $4
Green Grow 2 3
The company has a daily budge 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 selling price is $9 per pound for Super Two and $7 per pound 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 profit.
a. Formulate a linear programming model for this problem.
b. Solve the model using the computer.