Gastineau Corporation's two products have the following characteristics: The constrained resource is a particular machine that is available for 9, 600 minutes each month.Each unit of product J45Z requires 19 minutes on this machine and each unit of product W47E requires 7 minutes on this machine. Up to how much should the company be willing to pay to obtain enough of the constrained resource to satisfy demand for the two existing products?

Question

Gastineau Corporation's two products have the following characteristics:  The constrained resource is a particular machine that is available for 9, 600 minutes each month.Each unit of product J45Z requires 19 minutes on this machine and each unit of product W47E requires 7 minutes on this machine. Up to how much should the company be willing to pay to obtain enough of the constrained resource to satisfy demand for the two existing products?

Quizplus · Accepted Answer

To determine the maximum amount the company should be willing to pay per minute for the constrained resource, we need to calculate the contribution margin per minute for each product.

For product J45Z: 
Contribution margin per unit = $108 - $75 = $33 
Machine time per unit = 19 minutes 
Contribution margin per minute = $33/19 = $1.74

For product W47E: 
Contribution margin per unit = $72 - $45 = $27 
Machine time per unit = 7 minutes 
Contribution margin per minute = $27/7 = $3.86

To maximize profit, the company should allocate the constrained resource to the product with the higher contribution margin per minute. Therefore, the company should be willing to pay up to the amount that would make the contribution margin per minute for product J45Z equal to the contribution margin per minute for product W47E:

$1.74 + (x/19) = $3.86 + (x/7) 
Solving for x, we get x = $3 per minute

Therefore, the company should be willing to pay up to $3 per minute for the constrained resource. Choice B is the best answer.

Gastineau Corporation's Two Products Have the Following Characteristics: the Constrained