Question

A demand function for a certain product is given by the equation q = 1200 - 5p, where p is the price in

dollars, and q is the quantity demanded. Find a function to represent the revenue generated by producing
and selling q items. Use this function to determine the quantity that maximizes revenue. What price
should be charged in order to maximize revenue?

Answer 1

The revenue function is R(q) = pq = q * (1200 - q) / 5. To maximize revenue, calculate q by setting the derivative of R(q) to zero, resulting in q = 600. The price to charge for maximum revenue is $120.

Step-by-step explanation:

To find a function representing the revenue (R) generated by producing and selling q items, we multiply the quantity by the price. The demand function is given by q = 1200 - 5p, so to express revenue as a function of q, we need to solve for p first, which gives us p = (1200 - q) / 5. We then find the revenue function R(q) = pq = q * (1200 - q) / 5.

Now to maximize revenue, we differentiate R(q) with respect to q and set the derivative equal to zero: dR/dq = 1200/5 - 2q/5 = 0. Solving this, we find q = 600.

To find the price that maximized revenue, we plug q = 600 back into the demand function to get p = (1200 - 600) / 5, which simplifies to p = $120. Therefore, the price that should be charged to maximize revenue is $120.