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)

The company’s revenue function, R(x).
a) R(x) = 300x - 2x²
b) R(x) = 5000 + 40x
c) R(x) = 300 - 2x
d) R(x) = 40x - 300

The company’s expense function, E(x).

The company’s profit function, P(x).

If the company produced 750 bikes in a month, how much profit would the company make?

Answer 1

The expense function is E(x) = 5000 + 40x. The profit function is P(x) = (300 - 2x)x - (5000 + 40x). If the company produced 750 bikes in a month, the profit would be $60,000.

Step-by-step explanation:

The expense function accounts for both fixed and variable costs, where the fixed cost of $5000 is added to the variable cost of $40 per bike multiplied by the quantity produced (x). This gives the expense function E(x) = 5000 + 40x. To derive the profit function, subtract the expense function from the revenue function. The revenue function, R(x), is given by the price function (p(x)) multiplied by the quantity produced (x), resulting in R(x) = (300 - 2x)x. Subtracting the expense function from the revenue function yields the profit function P(x) = (300 - 2x)x - (5000 + 40x).

When evaluating the profit for producing 750 bikes, substitute x = 750 into the profit function: P(750) = (300 - 2 * 750) * 750 - (5000 + 40 * 750). Simplifying this equation, P(750) = $60,000. Therefore, producing 750 bikes in a month would result in a profit of $60,000 for Earl’s Biking Company. This profit is obtained by considering the costs of production, the revenue generated from selling bikes, and the fixed expenses incurred by the company.