Profit Maximization with Cost Function C(Q)=320+2Q+0.2Q^2 and Inverse Demand P=44−0.5Q

Profit Maximization with Cost Function C(Q) = 50 + 4Q + Q^2 and Inverse Demand P = 100 - 2Q

Profit Maximization for a Bicycle Manufacturer

A company's production costs are described by the total cost function C(Q) = 10Q + 50, and the market demand for its product is represented by the inverse demand function P = 70 - Q. To maximize its profit, what quantity (Q*) should the company produce, and what price (P*) should it charge?

Calculating Optimal Price and Quantity

A firm knows its total cost function and the market's inverse demand function. To find the specific price and quantity that will maximize its profit, it must follow a specific sequence of calculations. Arrange the following steps in the correct logical order.

A firm's production costs are described by the function C(Q) = 20 + 10Q + Q², and the market demand for its product is represented by the inverse demand function P = 70 - 2Q. An analyst correctly determines that the profit-maximizing quantity is Q* = 10. However, in their final step, they calculate the profit-maximizing price to be P* = $220. Which statement best describes the error made in calculating the price?

Evaluating a Suboptimal Production Decision

A firm's production process is described by the total cost function C(Q) = 100 + 4Q². The firm faces a linear inverse demand curve of the form P = A - 2Q, where 'A' is a positive constant representing the maximum possible price. If the firm sets its price at the profit-maximizing level of P* = $80, what must be the value of the constant 'A'?

Impact of a Demand Shift on a Firm's Pricing Strategy

A firm operates with a total cost function C(Q) = 5Q² + 10Q + 50 and faces an inverse demand function P = 100 - 5Q. A consultant advises the firm that to maximize profit, they should produce a quantity of 10 units.

For each firm described by a unique pair of cost and inverse demand functions, match it with its correct profit-maximizing output quantity (Q*).