Question

Bruce Corporation makes four products in a single facility. These products have the following unit product costs:

	Products
	A		B		C		D
Direct materials	$	14.80	$	10.70	$	11.50	$	11.10
Direct labor		19.90		27.90		34.10		40.90
Variable manufacturing overhead		4.80		3.20		3.10		3.70
Fixed manufacturing overhead		27.00		35.30		27.10		37.70
Unit product cost		66.50		77.10		75.80		93.40

Additional data concerning these products are listed below.

	Products
	A		B		C		D
Grinding minutes per unit		4.30		5.80		4.80		3.90
Selling price per unit	$	76.60	$	94.00	$	87.90	$	104.70
Variable selling cost per unit	$	2.70	$	1.70	$	3.80	$	2.10
Monthly demand in units		4,500		4,500		3,500		2,500

The grinding machines are potentially the constraint in the production facility. A total of 71,400 minutes are available per month on these machines.

Direct labor is a variable cost in this company.

Up to how much should the company be willing to pay for one additional minute of grinding machine time if the company has made the best use of the existing grinding machine capacity? (Round your intermediate calculations to 2 decimal places.)

Answer 1

Solution:

Computation of contribution margin per unit of constrained resource
Particulars	Product A	Product B	Product C	Product D
Selling price per unit	$76.60	$94.00	$87.90	$104.70
Variable cost per unit:
Direct material	$14.80	$10.70	$11.50	$11.10
Direct labor	$19.90	$27.90	$34.10	$40.90
Variable manufacturing overhead	$4.80	$3.20	$3.10	$3.70
Variable selling cost	$2.70	$1.70	$3.80	$2.10
Contribution margin per unit	$34.40	$50.50	$35.40	$46.90
Grinding minutes per unit	4.3	5.8	4.8	3.9
Contribution margin per minute of grinding machine	$8.00	$8.71	$7.38	$12.03

Company will first allocate the resources to Product D as it is offering highest contribution margin per minute of grinding machine, then to product B, A and C respectively.

Grinding machine time used for production of:

Product D = 2500 * 3.90 = 9750 minutes

Product B = 4500*5.80 = 26100 minutes

Product A = 4500*4.3 = 19350

Available time = 71400 - (9750 + 26100 + 19350) = 16200 minutes

Maximum possible units of product C = 16200 / 4.80 = 3375 units

Therefore in order to meet demand of Product C, company is willing to pay maximum $7.38 per minute of grinding machine time.