CAT 2003 Slot 1 — QA Question 9
A leather factory produces two kinds of bags, standard and deluxe. The profit margin is Rs. 20 on a standard bag and Rs. 30 on a deluxe bag. Every bag must be processed on machine A and on machine B. The processing times per bag on the two machines are as follows:
The total time available on machine A is 700 hours and on machine B is 1250 hours. Among the following production plans, which one meets the machine availability constraints and maximizes the profit?
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Answer & solution
Correct answer: Standard 75 bags, Deluxe 80 bags
Standard 75 bags, Deluxe 80 bags
- B
Standard 100 bags, Deluxe 60 bags
- C
Standard 50 bags, Deluxe 100 bags
- D
Standard 60 bags, Deluxe 90 bags
Total time available is 700 hrs on machine A and 1250 hrs on machine B.
Let the number of Standard Bags be s and the number of Deluxe Bags be d.
Here we have to maximize the profit margin i.e. 20s + 30d, subject to the constraints,
4s + 5d ≤ 700 and 6s + 10d ≤ 1250
Now consider options.
1. s = 75 and d = 80
∴ The profit = 75 × 20 + 30 × 80 = 3900
4s + 5d = 700 and 6s + 10d = 1250
∴ the constraints are satisfied.
2. s = 100 and d = 60
∴ The profit = 100 × 20 + 60 × 30 = 3800
The profit is less than in option 1.
∴ Option 2 is not the answer.
3. s = 50 and d = 100
∴ The profit = 50 × 20 + 100 × 30 = 4000
4s + 5d = 700 and 6s + 10d = 1300
∴ The second constraint is not satisfied.
∴ Option 3 cannot be the answer.
4. s = 60 and d = 90
∴ The profit = 60 × 20 + 90 × 30 = 3900
4s + 5d = 690 and 6s + 10d = 1260
∴ The second constraint is not satisfied.
∴ Option 4 cannot be the answer.
As only option 1 satisfies the constraints and also maximizes the profit, option 1 is the answer.
Hence, option (a).