LINEAR PROGRAMMING PROBLEM Consider the following linear pro

LINEAR PROGRAMMING PROBLEM. Consider the following linear programming model:

Minimize cost =       20A + 25B + 30C

Subject to:

Constraint 1,       9A + 14B – 7C 44

Constraint 2,       0.6A + 0.6B + 0.6C 10

Constraint 3,       A 15

Constraint 4,       B 10

A, B and C 0

Determine the number of units of A, B and C which satisfy the model using Excel as shown in the example setup on page 6 and Solver. Upload excel spreadsheet with results to the Final Exam Dropbox.

A) A units:   ___________

B) B units:    ___________

C) C units:    ___________

D) Minimum Cost:___________

Solution

linear programming model minimize cost = 20A + 25B +30C

Given 9A + 14B -7c <= 44

0.6A + 0.6B +0.6C <=10

A +B +C < = 16.66

A<= 15 , B>=10 ,

The A + B+C = 16.66

substituting the maximum values of A and b in equation

9(15) + 14(10) - 7c = 44

135 + 140 -7c = 44

c=33

Minimum cost = 20(15) + 25(10) + 30(33)

= 1540

The plot is as shown