A small company makes three different types of bird houses. Each type requires the services of three different departments, as indicated by the following table. Type A Type B Type C Cutting department 0.2 hour 0.1 hour 0.3 hour Finishing department 0.5 hour 0.5 hour 0.4 hour Assembly department 0.1 hour 0.1 hour 0.3 hour The cutting, finishing, and assembly departments have available a maximum of 61, 128, and 52 work-hours per week, respectively. How many bird houses of each type should be made per week so that the company is operating at full capacity?
A) 70 houses of type A, 60 houses of type B, and 100 houses of type C
B) 90 houses of type A, 70 houses of type B, and 120 houses of type C
C) 80 houses of type A, 60 houses of type B, and 100 houses of type C
D) 90 houses of type A, 60 houses of type B, and 110 houses of type C

Question

Quizplus · Accepted Answer

Let x, y, and z be the number of Type A, Type B, and Type C bird houses made per week, respectively.

The constraints are:
0.2x + 0.1y + 0.3z ≤ 61
0.5x + 0.5y + 0.4z ≤ 128
0.1x + 0.1y + 0.3z ≤ 52

The objective function is to maximize the total number of bird houses: 
maximize x + y + z

Using a linear programming solver, we get the following optimal solution:
x = 90
y = 70
z = 120

Therefore, the company should make 90 houses of type A, 70 houses of type B, and 120 houses of type C per week to operate at full capacity.

A Small Company Makes Three Different Types of Bird Houses