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.
Answer & explanation
Correct answer: option 4
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:
-
Wood constraint:
4x + 5y ≤ 200 -
Labour constraint:
3x + 6y ≤ 150 -
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
$=15,000$