The Kalo Fertilizer Company makes a fertilizer using two chemicals that provide nitrogen, phosphate, and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, whereas a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phosphate, and 1 ounce of potassium. Ingredient 1 costs $3 per pound, and ingredient 2 costs $5 per pound. The company wants to know how many pounds of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 20 ounces of nitrogen, 36 ounces of phosphate, and 2 ounces of potassium while minimizing cost.
Formulate a linear programming model for this problem.
Solve this model by using graphical analysis.
make a table
The value of the objective function at each of these extreme points is as follows:
|Objective function value
The minimum value of the objective function z=22 occurs at the extreme point (4,2).
Hence, the optimal solution to the given LP problem is: x=4,y=2, and min z=22
4 pound of ingredient 1
2 pound of ingredient 2
minimum cost is $22
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