Question

Earl's Biking Company manufactures and sells bikes. Each bike costs $40 to make, and the company's fixed costs are $5000. In addition, Earl knows that the price of each bike comes from the price function, p(x) = 300 - 2x (x = quantity produced).

Determine:

The company's revenue function, R(x).
The company's expense function, E(x).
The company's profit function, P(x).

Answer 1

Earl's Biking Company's revenue function is R(x) = x × (300 - 2x), the expense function is E(x) = 40x + 5000, and the profit function is P(x) = x(300 - 2x) - (40x + 5000).

Step-by-step explanation:

To calculate the revenue function, expense function, and profit function for Earl's Biking Company, we need to use some basic concepts from algebra and economics.

Revenue Function, R(x)

The revenue function is found by multiplying the number of items sold (x) by the price function (p(x)).

So, R(x) = x × p(x) = x × (300 - 2x).

Expense Function, E(x)

The expense function includes both variable costs and fixed costs.

The variable cost per bike is $40, so for x bikes, the variable costs are 40x.

Adding the fixed costs of $5,000, we get E(x) = 40x + 5000.

Profit Function, P(x)

To determine profit, we subtract expenses from revenue,

thus P(x) = R(x) - E(x)

= x(300 - 2x) - (40x + 5000).