Question

Required information [The following information applies to the questions displayed below.) 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-1 124 62 Price per unit Variable cost per unit Machine hours per unit Maximum units demand per period X-2 $ 224 $ 131 2.5 162,000 X-3 $ 448 $ 264 4.0 38,000 1.0 330,000 The single machine used for all three products has a maximum capacity of 618,000 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 354,000 hours (instead of 618,000 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

Particulars	x-1	x-2	x-3
Price per unit (A)	124	224	448
Variable Cost per unit (B)	62	131	264
Contribution per unit (C=A-B)	62	93	184
Machine hours per unit (given) (D)	1	2.5	4
Contribution per Machine hour (E = C/D)	62	37.2	46
Rank (based on E)	1st	3rd	2nd

Rank	Product	Maximum units demanded	Hours reqd	Balance remaining
	Total hours available			618000
1	x-1	330000	330000*1 = 330000	288000
2	x-3	38000	38000*4 = 152000	136000
3	x-2	162000	162000*2.5 = 405000	-269000

Since Maximum hours are limited, we produce maximum of x-2 => 136000 hours /2.5 hours per unit = 54400 units.

So,

a.

Particulars	x-1	x-2	x-3
units produced	330000	54400	38000

b. The maximum Clarke would be willing to pay would be equal to the contribution per hour of the product with unmet demand ie., x-2

The maximum for 20 hours Clarke would be willing to pay is 20 hours * 37.5 $ = 750 $.

c. If maximum hours were 354000:

Rank	Product	Maximum units demanded	Hours reqd	Balance remaining
	Total hours available			354000
1	x-1	330000	330000	24000

Hence, the second product with higher contribution per machine hour is x-3 So, 24000 hrs/ 4 = 6000 units.

Unmet demands are for x-3 (38000-6000 = 32000) and x-2 162000. So we use the 20 hours for either x-3 or x-2. Maximum under x-3 will be 46*20 = 920 $ or 750 $ (as computed above in b). Hence the maximum clarke is willing would be 920 $ for 20 hours.

d. No bottleneck would mean sufficient quantity to meet all demands. Accordingly,

	A	B	A*B
	Hours per unit reqd	Total Demand	Total Hours required
x-1	1	330000	330000
x-2	2.5	162000	405000
x-3	4	38000	152000
		Total Demand	887000

Hence if Machine Hours available are equal or more than 887000 hours, we wont have any bottlenecks.

Please comment in case of any query regarding the solution.