Question

Solve the linear program below with python.

OBJECTIVE FUNCTION::

Maximize Contribution Z=40X+26Y+66Z

CONSTRAINTS:

Cutting Capacity =1800min.

4X+8Y+4Z< or =1800

Stitching Capacity =2100 min

6X+6Y+4Z< or=2100

Pressing Capacity=1500 min.

6X+8Y+6Z< or =1500

Maximize : Z=40X+26Y+66Z

Constraints:

4X+8Y+4Z< or =1800

6X+6Y+4Z< or=2100

6X+8Y+6Z< or =1500

Answer 1

import numpy as np
A = np.array([[4, 8, 4], [6, 6, 4], [6, 8, 6]])#array A as a 3 by 3 array of the coefficients
b = np.array([1800, 2100, 1500])#array b as the right-hand side of the equations
r = np.linalg.solve(A, b)#Solve for the values of x, y and z using np.linalg.solve(A, b)
print("The result set is",r)
x=r[0]#storing the value of x from the result set to variable x
y=r[1]#storing the value of y from the result set to variable y
z=r[2]#storing the value of z from the result set to variable z
Z=(40*x)+(26*y)+(66*z)
print("Z is equal to ",Z)

The below photo shows the execution of this problem in jupyter notebook.