Question

A company produces a commodity with 36,000 as a fixed cost. The variable cost is estimated to be 25% of the total revenue earned. The selling price of the product is 20 per unit.

Find the following:

1. Cost function
2. Profit function

Answer 1

(a) Cost function:

Total cost = Fixed Cost + Variable Cost

Total cost = 36000 + 25% of total revenue

= 36000 + `25/100 × 20x` 

∴ Total cost = 36000 + 5x

(b) Profit function

Profit function = Total Revenue − total Cost

= 20x − (36,000 + 5x)

= 20x − 36,000 − 5x

= P(x) = 15x − 36,000