In [ ]: #Your Function should return A, b, c, and X matrices def Compaq(equations, objective_function): #INPUT: equation: string #OUTPUT:

Production planning by Compaq

This is a problem that Compaq had faced illustrating the usefulness of linear optimization. Compaq introduced three new computer systems and two workstations: GP-1, GP-2, and GP-3, as well as WS-1 and WS-2. In the following table, we list the models, the list prices (in dollars), and the memory usage.

SystemPrice#256K BoardsGP-160,0004GP-240,0002GP-330,0002WS-130,0002WS-215,0001

The following dificulties were anticipated:

1. The in-house supplier of CPUs could provide at most 7,000 units, due to debugging problems.
2. The supply of 256K memory boards was limited to be no more than 8,000 units.

On the demand side, the marketing department established the following:

1. The maximum demand for the first quarter would be 1,800 for GP-1 system, 300 for GP-3 system, 3,800 for the whole GP, and 3,200 for the whole WS family.
2. Included in these projects were 500 orders for GP-2 system, 500 orders for WS-1, and 400 orders for WS-2 that had already been received and had to be fulfilled in the first quarter.

Compaq needed to make a production plan to consider all the above production limitations and demand projections and to maximize the revenue.

Linear Model for Compaq

The above problem can be reformulated as:

maxa∗60000+b∗40000+c∗30000+d∗30000+e∗15000

maxa∗60000+b∗40000+c∗30000+d∗30000+e∗15000

subject to the constraintsa+b+c+d+e<=7000

a+b+c+d+e<=7000

4a+2b+2c+2d+e<=8000

4a+2b+2c+2d+e<=8000

a+b+c<=3800

a+b+c<=3800

d+e<=3200

d+e<=3200

a<=1800

a<=1800

c<=300

c<=300

b>=500

b>=500

d>=500

d>=500

e>=400

e>=400

Also, keep in mind

maxc

T

x=−min(−c

T

x)

maxcTx=−min(−cTx)

and minimization is the standard form of a Linear Program

Your task will be to solve the above problem, and maximize Compaq's profits. Complete the Compaq function to maximize Compaq's profits. Use the ConvertToStandardNormalForm function to help you. The matrices formed will be passed into a linear program solver to output the best solution.

Hint: Keep in mind that since this is a maximization problem, each value of matric c will have to be multiplied by -1 to bring it into standard form (please ignore the minus sign '-' outside the minimization expression, this will be accounted for in the solution).

In [ ]: #Your Function should return A, b, c, and X matricesdef Compaq(equations, objective_function):#INPUT: equation: string#OUTPUT: Matrices c, b, and A## YOUR CODE HERE#return A,b,c