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:
Let \(x\) = number of standard bags, \(y\) = number of deluxe bags.
Constraints:
Machine A: \(4x + 5y \le 700\)
Machine B: \(6x + 10y \le 1250\)
Profit: \(P = 20x + 30y\)

Step 2:
Option 1: \(x=100, y=60\)
A: \(400 + 300 = 700\) (valid)
B: \(600 + 600 = 1200 \le 1250\) (valid)
Profit = \(2000 + 1800 = 3800\)

Option 2: \(x=75, y=80\)
A: \(300 + 400 = 700\) (valid)
B: \(450 + 800 = 1250\) (valid)
Profit = \(1500 + 2400 = 3900\)

Option 3: \(x=100, y=10\)
A: \(400 + 50 = 450 \le 700\)
B: \(600 + 100 = 700 \le 1250\)
Profit = \(2000 + 300 = 2300\)

Option 4: \(x=60, y=90\)
A: \(240 + 450 = 690 \le 700\)
B: \(360 + 900 = 1260 > 1250\) (violates)

Option 5: \(x=50, y=100\)
A: \(200 + 500 = 700\)
B: \(300 + 1000 = 1300 > 1250\) (violates)

Step 3:
Option 2 gives the highest profit (3900) while satisfying all constraints.

Step 4:
Final Answer: Standard = 75 bags, Deluxe = 80 bags