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 constraint) in the production process is upholstery labor-hours. Information concerning three of Portsmouth's upholstered chairs appears below:

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 constraint) 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	$	1,380		$	1,890		$	1,575
Variable cost per unit	$	900		$	1,350		$	1,150
Upholstery labor-hours per unit	8 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 $42 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 if it hires the nearby upholstering company to make Love Seats?

3. Should Portsmouth hire the nearby upholstering company?

 

Explanation

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	$	1,890
Variable cost per unit		1,350
Contribution margin per unit (a)	$	540
Upholstery shop time required to produce one unit (b)	12 hours
Contribution margin per unit of the constrained resource (a) ÷ (b)	$45 per hour

The company should be willing to pay an overtime premium of up to $45 per hour to keep the upholstery shop open after normal working hours.

2.

To answer this question, it is desirable to compute the contribution margin per unit of the constrained resource for the Love Seat:

	Love Seat
Selling price per unit	$	1,575
Variable cost per unit		1,150
Contribution margin per unit (a)	$	425
Upholstery shop time required to produce one unit (b)	5 hours
Contribution margin per unit of the constrained resource (a) ÷ (b)	$85 per hour

The additional contribution margin per hour earned by hiring the nearby company is $43 ($85 – $42).

3.

The offer by the nearby upholstering company to upholster furniture for $42 per hour should be accepted. The time would be used to upholster Loveseats. If this increases the total production and sales of Loveseats, the time would be worth $85 per hour—a net gain of $43 per hour. If Loveseats are already being produced up to demand, then having these units upholstered in the other company would free up capacity to produce more of the other two product-lines. In both cases, the additional time is worth more than $42 per hour.

Thanks