Question

A carpenter makes tables and chairs. Profit per table is Rs. 200 and that per chair is Rs. 100. He should make at least two chairs per table and the total number of tables and chairs should not exceed 30. Find the maximum profit.​

Answer 1

profit on 1 table = 200

profit on 2 chairs = 200

so the maximum profit = 30 x 400 = 12000

so his maximum profit is ₹12000

Answer 2

The maximum profit that the carpenter can make is Rs. 4000.

Given:

Profit per chair = Rs. 100

Profit per table = Rs. 200

Number of chairs = 2 × Number of tables

The number of chairs and tables must not exceed 30.

To Find:

We need to find the maximum profit

Solution:

Let the number of chairs be x and the number of tables be y

Profit = 100x + 200y

Also, x = 2y

and x + y ≤ 30

⇒ 2y + y ≤ 30

y ≤ 10

Thus, the maximum number of tables that can be produced is 10

⇒ x = 20

Substituting these values in the profit equation, we get-

Profit = (100 × 20) + (200 × 10)

= 2000 + 2000

= 4000

Thus, the maximum profit that the carpenter can make is Rs. 4000.

#SPJ3