Question

# Linear Programming/ Finite Mathematics A plant produces two types of cereals, corn flake and cheerios oat...

Linear Programming/ Finite Mathematics

A plant produces two types of cereals, corn flake and cheerios oat crunch.   The chocolate chip cookies sell for \$70 per case, and the oatmeal raisin cookies sell for \$65 per case.

There are three machines in the plant that can make either type of the cereals. The machines are label A, B, and C. The maintenance crews set up the machines to operate for 16 hours a day

Machine” A” takes 1/4 of an hour to make a case of corn flake, and 1/4 of an hour to make a case of cheerios oat crunch.

Machine “B” takes 1/3 hour to make a case of corn flake, and 1/6 of an hour to make a case of cheerios oat crunch.

Machine “C” takes 1/7 of an hour to make a case of corn flake, and 2/7 of an hour to make a case of cheerios oat crunch.

PART ONE:

Construct a linear programming problem that tells the number of cases of each type of cereals that maximizes the sales. Construct the objective function and constraints. (HINT: Let x be the number of cases of corn flake, and y be the number of cases of cheerios oat crunch. Identify the corner points of the feasible region and compare each point with the objective function to determine the maximum sales.

PART TWO:

It is determined that the cost of running each machine per hour is as follow; Machine A costs \$70 per hour to operate, Machine B costs \$90 per hour to operate, and Machine C costs \$120 per hour to operate. The setup and cleanup crews at the beginning and end of each day cost the company \$300.