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 $5,000$

cases of paper. There is only enough stock to make $4,000$ cases of

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

are produced with the same machine and $1,200$ hours of machine time are

available. Premium paper takes $18$ minutes per case to produce and

ordinary paper takes $12$ 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?