Question

A manufacturer makes two types of handmade fancy paper bags: type A and type B. Identify the number of bags of each type to be manufactured to obtain maximum profit.

Answer 1

Let a represent the number of bag A

Let b represent the number of bag B

From the information given,

A type A bag requires 2 hours o the cutter's time while type B requires 3 hours of the cutter's time.The total time the cutter is available is 108 hours. The inequality representing the total number of hours for the cutter is

2a + 3b ≤ 108

A type A bag requires 3 hours o the finisher's time while type B requires 1 hour of the finisher's time.The total time the cutter is available is 78 hours. The inequality representing the total number of hours for the finisher is

3a + b ≤ 78

We would plot these inequalities. The graph is shown below

The solution region is the purple region. The boundary lines are shown as well

The equation for the profit is

12a + 9b

We would substitute the values in the graph and select the maximum

For (0, 36),

Profit = 12(0) + 9(36) = 324

For (18, 24),

Profit = 12(18) + 9(24) = 432

For (26, 0),

Profit = 12(26) + 9(0) = 312

Thus, the correct option is C