Linear Programming Application

Nayan M Truong

A print shop at a community college in Cupertino, California, employs two different contractors to maintain its copying machines. The print shop needs to have $14$ IBM, $18$ Xerox, and $24$ Canon copying machines serviced. Contractor A can repair $2$ IBM, $1$ Xerox, and $2$ Canon machines at a cost of $$950$ per month, while Contractor B can repair $1$ IBM, $3$ Xerox, and $2$ Canon machines at a cost of $$975$ per month. How many months should each of the two contractors be employed to minimize cost?

a$.$ Of the options below, give the number that represents

the correct set of variables

the correct objective function description

the correct set of constraint descriptions

the number of months to employ contractors A and $B$

the number of customers who use each type of copier in the print shop

the number of copiers to maintain and the number each contractor can maintain

total cost of the maintenance contracts

b$.$ Letting $x$ be the first of the variables listed in the problem statement, and $y$ the second, write the objective function.

$z=$

c$.$ Graph the feasible region on paper, then list the corner points of the feasible region.

$($Enter ordered pairs $(x,y),$ separated by commas.$)$

d$.$ Test the corner points to find the optimum value of the objective function:

The "winning" corner point is

The optimum value of the objective function is