Madison Box Company makes medium and large wooden boxes. Medium boxes require 9

Question

Madison Box Company makes medium and large wooden boxes. Medium boxes require 9 square feet of wood, while large ones consume 12 square feet of wood. All boxes require 0.5 labor hour regardless of size. Wood is limited to 400 square feet daily and only 20 labor hours are available each day. Due to space limitations, no more than 10 large boxes can be made each day. Also, customers can absorb at most 30 medium boxes. Medium boxes yield a profit of $11 each, and large ones yield $15 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 Madison the optimal profit.

Explanation / Answer

Decision variables:

Let X = No of Medium wooden boxes to be produced

Y = No of large wooden boxes to be produced

Objective function is to maximize profits

Z = max 11X + 15Y

Constraints:

9X + 12Y <= 400 (Wood available)

0.5X+0.5Y<=20 (Labor hours)

Y<= 10

X<= 30

X,Y>=0

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