Question

Required information [The following information applies to the questions displayed below.) Clarke Corporation manufactures th

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?

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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.

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