Question

( Management Science MGT 397 ) Class.

General Packaging Company makes medium and large wooden boxes. Medium boxes require 16 square feet of wood, while large ones consume 25 square feet of wood. Each medium box requires 0.25 labor hour, and each large box requires 0.30 labor hours to produce. Wood is limited to 500 square feet daily and only 40 labor hours are available each day. Due to space limitations, no more than 20 large boxes can be made each day. Also, customers can absorb at most 36 medium boxes. Medium boxes yield a profit of $12 each, and large ones yield $16 profit each. Formulate this problem as a linear programming model, to determine the number of each size of box to produce daily, that will give General Packaging Company the optimal profit.

Answer 1

Let Quantity of medium box be =X

Let Quantity of medium box be=Y

Objective function(Maximization)=12X+16Y

For wood , 16x+25y450

For labour 0.25x+0.3040

X36

Y20