Question

Clarke Corporation manufactures three products (X-1, X-2, and X-3) utilizing, in one of the processes, a single machine for all products. Data on the individual products follow.

	X-1			X-2			X-3
Price per unit	$	160		$	260		$	520
Variable cost per unit	$	80		$	140		$	300
Machine hours per unit		1.0			2.5			4.0
Maximum units demand per period		375,000			180,000			65,000

The single machine used for all three products has a maximum capacity of 798,000 hours per period.

Required:

a. How many units of each product should be produced each period?

b. A local engineering firm has suggested to Clarke that it might be able to increase the capacity on the machine. What is the maximum Clarke would be willing to pay for an increase of twenty (20) machine hours?

c. Suppose the maximum capacity on the machine was 435,000 hours (instead of 798,000 hours). What is the maximum Clarke would be willing to pay for an increase of twenty (20) machine hours?

d. At what capacity (in machine hours) would the machine no longer be a bottleneck?

Answer 1

Product with maximum contribution margin per unit of bottleneck should be produced first
Calculation of contribution margin per machine hour
	X-1	X-2	X-3
Price per unit	160	260	520
Variable cost per unit	80	140	300
Contribution Margin per Unit	80	120	220
Machine hours per unit	1	2.5	4
Contribution Margin per Machine hour	80	48	55
Production Schedule
Product	Number of Units	Machine Hours per Unit	Total Machine Hours
X-1	375,000	1	375,000
X-2	65,200	2.5	163,000
X-3	65,000	4	260,000
		Total	798,000
Maximum for increase = contribution margin earned = 20*48 = $960
c.Increased machine hours will be used to produce X-3, hence amount paid = 20*55 = $1100
d.Capacity in machine hours = 375,000+260,000+180,000*2.5 = 1,085,000 hours
i.e. when demand for all products will be met