Question

Read the following passage carefully and answer the question that follows: 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: |c|c|c| Time Required in Hours per Bag & Machine A & Machine B
Standard Bag & 4 & 6
Deluxe Bag & 5 & 10
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 profits for the factory?

• A. Standard 100 bags, Deluxe 60 bags
• B. Standard 75 bags, Deluxe 80 bags
• C. Standard 100 bags, Deluxe 10 bags
• D. Standard 60 bags, Deluxe 90 bags
• E. Standard 50 bags, Deluxe 100 bags

Hint:

Check each options against the constraints and calculate profit to find the maximum.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a Linear Programming problem. We need to check which plan stays within the machine hour limits while providing the highest profit.
Step 2: Key Formula or Approach:
Constraints: 1. Machine A: \(4S + 5D \le 700\) 2. Machine B: \(6S + 10D \le 1250\) Profit = \(20S + 30D\).
Step 3: Detailed Explanation:
Let's check the options for feasibility: - (A) 100S, 60D: \(4(100)+5(60)=700\) (OK); \(6(100)+10(60)=1200\) (OK). Profit = \(2000+1800=3800\). - (B) 75S, 80D: \(4(75)+5(80)=300+400=700\) (OK); \(6(75)+10(80)=450+800=1250\) (OK). Profit = \(1500+2400=3900\). - (D) 60S, 90D: \(4(60)+5(90)=240+450=690\) (OK); \(6(60)+10(90)=360+900=1260\) (NOT OK). - (E) 50S, 100D: \(4(50)+5(100)=700\) (OK); \(6(50)+10(100)=1300\) (NOT OK). Comparing valid plans: Plan B (3900) is higher than Plan A (3800).
Step 4: Final Answer:
Standard 75 bags, Deluxe 80 bags maximizes profit.