Question

Portsmouth Company makes upholstered furniture. Its only variable cost is direct materials. The demand for the company's products far exceeds its manufacturing capacity. The bottleneck (or constriant) in the production process is upholstery labor-hours. Information concerning three of Portsmouth's upholstered chairs appears below:

	Recliner			Sofa			Love Seat
Selling price per unit	$	1,320		$	1,960		$	1,450
Variable cost per unit	$	800		$	1,300		$	1,050
Upholstery labor-hours per unit	10 hours			12 hours			5 hours

Required:

1. Portsmouth is considering paying its upholstery laborers additional compensation to work overtime. Assuming that this extra time would be used to produce sofas, up to how much of an overtime premium per hour should the company be willing to pay to keep the upholstery shop open after normal working hours?

2. A small nearby upholstering company has offered to upholster furniture for Portsmouth at a price of $51 per hour. The management of Portsmouth is confident that this upholstering company’s work is high quality and their craftsmen can work as quickly as Portsmouth’s own craftsmen on the simpler upholstering jobs such as the Love Seat. How much additional contribution margin per hour can Portsmouth earn if it provides the raw materials to the nearby company and then hires it to upholster the Love Seats?

3. Should Portsmouth hire the nearby upholstering company?

Answer 1

1) The value of relaxing the constraint can be determined by computing the contribution margin per unit of the constrained resource:

Sofa

Selling Price per unit $1,960

Variable cost per unit $1,300

Contribution margin per unit (a) $660

Upholstery shop time required to produce one unit (b) 12

Contribution margin per unit of the constrained resource (a) ÷ (b) = $660/12 = $55 per hour

the company be willing to pay up to $55 per hour overtime premium, to keep the upholstery shop open after normal working hours.

2.

	Recliner			Sofa			Love Seat
Selling price per unit	$	1,320		$	1,960		$	1,450
Variable cost per unit	$	800		$	1,300		$	1,050
Upholstery labor-hours per unit(b)	10 hours			12 hours			5 hours
Contribution margin per unit (a) $ 520 $660 $ 400   Contribution margin per unit of the constrained resource (a) ÷ (b) = $52 $ 55 $80 The offer to upholster chairs for $51 per hour should be accepted. The time would be used to upholster Loveseats. If this increases the total production and sales of those chairs, the time would be worth $80 per hour r—a net gain of $29 per hour . If Loveseats are already being produced up to demand, then having these chairs upholstered in the other company would free up capacity to produce more of the other two chairs. In both cases, the additional time is worth more than $51 per hour

$29 per hour additional contribution margin per hour Portsmouth earn if it provides the raw materials to the nearby company and then hires it to upholster the Love Seats.

3. Yes, Portsmouth should hire the nearby upholstering company.