Question

Past experience has shown manufacturers that the demand of a product is given by the equation p = 125 - 0.25q.State the Revenue function:

The revenue function can be determined by multiplying the price (p) by the quantity (q). Therefore, the revenue function is R = pq.
How many units must be sold to maximize revenue? What is the maximum revenue?
To find the number of units that must be sold to maximize revenue, we need to find the quantity (q) at which the derivative of the revenue function (R) with respect to quantity (q) is equal to zero. This will give us the maximum point on the revenue function.
To find the maximum revenue, we substitute the value of q that we found into the revenue function R = pq.

Answer 1

To maximize revenue given the demand equation p = 125 - 0.25q, we differentiate the revenue function R(q) = (125 - 0.25q)q and find that selling 250 units will maximize revenue. Substituting q=250 into the revenue function will then give the maximum revenue.

Step-by-step explanation:

The student's question revolves around finding the quantity to maximize revenue and what that maximum revenue would be, given the demand equation p = 125 - 0.25q. The revenue function is provided by R = pq. To find the quantity that maximizes revenue, we differentiate the revenue function with respect to q and set it to zero. From the given demand equation, the revenue function becomes R(q) = (125 - 0.25q)q. The derivative of R with respect to q is R'(q) = 125 - 0.5q, and setting R'(q) = 0 gives us the maximizing quantity 125 = 0.5q, or q = 250 units. Substituting this back into the revenue function will give us the maximum revenue.