Set up and solve the following Linear Programming Problem, being

sure to include slack and surplus variables:

Impact Printing makes two kinds of computer paper, premium quality and

ordinary quality. They have a contract to supply a total of at least

$5$

$,$

$0$

$0$

$0$

$$

cases of paper. There is only enough stock to make

$4$

$,$

$0$

$0$

$0$

$$cases of

premium paper, but ample stock for ordinary paper. Both kinds of paper

are produced with the same machine and

$1$

$,$

$2$

$0$

$0$

$$hours of machine time are

available. Premium paper takes

$1$

$8$

$$minutes per case to produce and

ordinary paper takes

$1$

$2$

$$minutes per case. If the profit for premium paper

is $

$4$

$$per case and for ordinary paper is $

$3$

$$per case, how many cases of

each kind of paper must be made and sold to maximize the profit?