Question

A manufacturer makes two types of handmade fancy paper bags. Type A and Type B. Two designers a cutter and a finisher need to work on both kinds of bags. A type A bag requires 2 hours of the cutters time and 3 hours of the finishers time. A type B bag requires 3 hours of the cutters time and 1 hour of the finishers time. Each month the cutter is available for 108 hours and the finisher is available 78 hours. The manufacturer gets a profit of $12 for each bag of type A and $9 for each bag of type B. Identify the number of bags for each type to be manufactured to obtain the maximum profit.

Answer 1

Answer:

• 18 Type A bags
• 24 Type B bags

Step-by-step explanation:

The graph shows the constraints and the boundaries of the feasible region. The maximum profit will be had with the manufacture of 18 Type A bags and 24 Type B bags.

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The inequality describing the constraint on cutter hours is ...

  2a +3b ≤ 108

The inequality describing the constraint on finisher hours is ...

  3a +1b ≤ 78

The boundary lines of the solution regions of these inequalities intersect at ...

  (a, b) = (18, 24)

The profit function is such that it doesn't pay to make all of one type or the other bags. The most profit is had for the mix ...

  18 Type A bags; 24 Type B bags.

On the graph, the line representing the profit function will be as far as possible from the origin at the point of maximum profit.