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?
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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