Homework SourseA small firm makes three products which all follow the same
A small firm makes three products, which all follow the same three step process, which consists of milling, inspection, and drilling. Product A requires 6 minutes of milling, 5 minutes of inspection, and 4 minutes of drilling; product B requires 2.5 minutes of milling, 2 minutes of inspection, and 2 minutes of drilling; and product C requires 5 minutes of milling, 4 minutes of inspection, and 8 minutes of drilling. The department has 20 hours available during the next period for milling, 15 hours for inspections, and 24 hours for drilling. Product A contributes $6 per unit to profit, product B contributes $4 per unit, and product C contributes $10 per unit.
At the optimum solution, what is the company\'s profit during the next period?
How many units of each are produced at the optimal solution (use numbers)?
Solution
Ans:
Hello friend, here is the answer of your question. I tried best to explain the answer below.
This is the question of limiting/key factor.
A key factor refers to the scarce in availability of production resources. It is a factor which puts a limit on production and profit of a business. In this question key factor is “TIME”
In this type of questions selection of product is based on Contribution per unit of limiting factor which is “TIME” in this question.
The product which contributes higher contribution towards limiting factor should be given priority than other.
So, in the question, first of all we need to calculate Contribution per minute of different products.
Calculation of total time required by each product
Product
Time requires by each product in following process
Total time taken by products
Milling
Inspection
Drilling
A
6 minutes
5 minutes
4 minutes
15 minutes
B
2.5 minutes
2 minutes
2 minutes
6.5 minutes
C
5 minutes
4 minutes
8 minutes
17 minutes
Calculation of Contribution per minute of each product and Ranking on the basis of Higher Contribution per minute
Product
Total time taken in three processes
Contribution per unit
Contribution Per Minute (Contribution per unit / Minutes)
Ranking
A
15 minutes
$6
$0.40
III
B
6.5 minutes
$4
$0.62
I
C
17 minutes
$10
$0.59
II
PRODUCT B HAS HIGHER CONTRIBUTION PER MINUTE THAN OTHER PRODUCTS. SO, FIRM SHOULD GO FOR MAKING PRODUCT B FIRST DUE TO HIGHER CONTRIBUTION THAN OTHER PRODUCTS.
CALCULATION OF OPTIMUM NO UNITS WHICH CAN BE PRODUCED OF EACH PRODUCT UNDER EACH PROCESS:
Milling
Inspection
Drilling
Maximum available minutes under each process
20 Hours or 1200 minutes
15 hours or 900 minutes
24 hours or 1440 minutes
Minutes required by Product B per unit under each process
2.5 minutes
2 minutes
2 minutes
No. of Units can be produced (Product B)
1200 / 2.5 = 480 Units
900 / 2 = 450 Units
1440 / 2 = 450 Units
OPTIMUM PRODUCTION UNIT OF PRODUCT B
450 UNITS
Minutes required by Product A per unit under each process
6 minutes
5 minutes
4 minutes
No. of Units can be produced (Product A)
1200 / 6 = 200 Units
900 / 5 = 180 Units
1440 / 4 = 360 Units
OPTIMUM PRODUCTION UNIT OF PRODUCT A
180 UNITS
Minutes required by Product C per unit under each process
5 minutes
4 minutes
8 minutes
No. of Units can be produced (Product C)
1200 / 5 = 240 Units
900 / 4 = 225 Units
1440 / 8 =180 Units
OPTIMUM PRODUCTION UNIT OF PRODUCT A
180 UNITS
FROM THE ABOVE CALCULATION, THE OPTIMUM PRODUCTION UNITS CAN BE PRODUCED WILL BE AS FOLLOWS:
PRODUCT A = 180 UNITS
PRODUCT B = 450 UNITS
PRODUCT C = 180 UNITS
AT OPTIMUM SOLUTOIN THE PROFIT TO THE FIRM FOR NEXT PERIOD = NO. OF UNITS OF PRODUCT B X CONTRIBUTION PER UNIT
PROFIT = 450 UNITS X $4 = $1800
| Product | Time requires by each product in following process | Total time taken by products | ||
| Milling | Inspection | Drilling | ||
| A | 6 minutes | 5 minutes | 4 minutes | 15 minutes |
| B | 2.5 minutes | 2 minutes | 2 minutes | 6.5 minutes |
| C | 5 minutes | 4 minutes | 8 minutes | 17 minutes |
