CAT 2003 Slot 1 — QA Question 9
Answer the following question based on the information given below.
New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved.
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?
âââââââ
Answer & solution
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).