A company that supplies water to a city faces a market demand curve of P = 120-2q. At what quantity does the company maximise total revenue?

The total revenue (TR) of a company is calculated by multiplying the price (P) it sells its product at by the quantity (q) of the product it sells. In this case, the price is given by the equation P = 120 - 2q.

So, the total revenue (TR) is given by the equation TR = P * q = (120 - 2q) * q = 120q - 2q^2.

To find the quantity that maximises total revenue, we need to find the quantity (q) that maximises this equation. This is done by taking the derivative of the total revenue equation with respect to quantity and setting it equal to zero, then solving for q.

The derivative of 120q - 2q^2 with respect to q is 120 - 4q.

Setting this equal to zero gives:

120 - 4q = 0 4q = 120 q = 120 / 4 q = 30

So, the company maximises total revenue when it sells a quantity of 30.