A future company manufactures two types of chairs: Basic Chairs and Luxury Chairs.

• Basic Chair Requirements 4 unit of wood and 3 hours of labour.
• Luxury Chair Requirements 5 unit of wood and 6 hours of labour.
• The company has limited resources of wood (200 units) and labour force (150 hours).
• Profit on Luxury chair = Rs. 200
• Profit on Basic chair = Rs. 300

Calculate the maximum profit.

15,000

The correct answer is Option (4) → 15,000

Let

• x = number of Basic Chairs

• y = number of Luxury Chairs

Objective Function (to maximize profit):

Z = 300x + 200y

Subject to constraints:

1. Wood constraint:
     4x + 5y ≤ 200

2. Labour constraint:
     3x + 6y ≤ 150

3. Non-negativity:
     x ≥ 0, y ≥ 0

 ∴ Optimal production → 50 basic chair only and 0 luxury chair.

$Z_{max}=Z(50,0)$

Maximize $Z=300x+200y$

Z=300×50+200×0

$=15,000$