Question

Profit function?

Answer 1

(a)

The Profit Function is P(x) = 30x - 140 - 0.2x²

Calculate Profit in selling 11 chairs, Substitute x = 11 in the Profit Function

P(11) = 30*11 - 140 - 0.2(11)²

P(11) = 330 - 140 - 24.2

P(11) = $165.8

Calculate Profit in selling 10 chairs, Substitute x = 10 in the Profit Function

P(10) = 30*10 - 140 - 0.2(10)²

P(10) = 300 - 140 - 20

P(10) = 140

Exact additional Profit = P(11) - P(10) = 165.8 - 140

Therefore Exact additional Profit in selling 11 chairs instead of 10 chairs is $ 25.8.

Answer 2

(b)

The Profit Function is P(x) = 30x - 140 - 0.2x²

Substitute x = 10 in the Profit Function

P(10) = 30*10 - 140 - 0.2(10)²

P(10) = 300 - 140 - 20

P(10) = 140

Therefore Marginal Profit is $140.