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	$	148		$	248		$	496
Variable cost per unit	$	74		$	137		$	288
Machine hours per unit		1.0			2.5			4.0
Maximum units demand per period		360,000			174,000			56,000

The single machine used for all three products has a maximum capacity of 738,000 hours per period.

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 408,000 hours (instead of 738,000 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	148	248	496
Variable cost per unit	74	137	288
Contribution Margin per Unit	74	111	208
Machine hours per unit	1	2.5	4
Contribution Margin per Machine hour	74	44.4	52
Production Schedule
Product	Number of Units	Machine Hours per Unit	Total Machine Hours
X-1	360,000	1	360,000
X-2	61,600	2.5	154,000
X-3	56,000	4	224,000
		Total	738,000
Maximum for increase = contribution margin earned = 20*44.4 = $888
c.Increased machine hours will be used to produce X-3, hence amount paid = 20*52 = $1040
d.Capacity in machine hours = 360,000+224,000+174,000*2.5 = 1,019,000 hours
i.e. when maximum demand of all products are met