Question

Solve the following LP problem using the Solver in MS Excel.

A farmer wants to customize his fertilizer for his current crop. He can buy plant food mix A and plant food mix B. Each cubic yard of food A contains 20 pounds of phosphoric acid, 30 pounds of nitrogen and 5 pounds of potash. Each cubic yard of food B contains 10 pounds of phosphoric acid, 30 pounds of nitrogen and 10 pounds of potash. He requires a minimum of 460 pounds of phosphoric acid, 960 pounds of nitrogen and 220 pounds of potash. If food A costs $30 per cubic yard and food B costs $35 per cubic yard, how many cubic yards of each food should the farmer blend to meet the minimum chemical requirements at a minimal cost? What is this cost?

Answer 1

Below is the LP Formulation and Excel solver solution -

LP Formulation

Minimize Costs Z = 30A+35B

s.t. constraints -

20A+10B >=460 ---> Phosporic acid

30A+30B >=960 ---> Nitrogen

5A+10B >=220 ---> Potash

A,B >= 0

Solver solution

Minimum cost = 1020 $

A = 20 cubic yards, B = 12 cubic yards