Linear programming

Question

Impact Printing makes two kinds of computer paper using premium or ordinary quality stock. They have a contract to supply at least 5000 cases of paper. There is only enough stock to make 4000 cases of premium paper, but ample stock for ordinary paper. Both kinds are made with the same machine and 7200 minutes of machine time are available. Premium paper takes 18 minutes per case to make and ordinary paper takes 12 minutes per case. The profit is $4/case and $3/case, respectively.

Answer 1

This is not a good question.

The optimum solution is to make all the ordinary cases possible. The bottle neck is in machine time at 7,200 minutes available the max production is 400 cases of premium or 600 cases of ordinary.

400 cases x $4= $1,600 for premium
600 cases X $3= $1,800 for ordinary.

The direct material is not a constraint.

The simplex algorithm equation would be;

Maximize Profit = $4 Premium + $3 Ordinary
                                  X               Y

 

Subject to                     1              1         >= 5,000 sales contract
                                   18             12       <= 7,200 Machine Time
                                    1                        <= 4,000 stock constraint

The sales contract constraint creates a situation where there is no solution
The stock constraint is irreverent.