[Jack17012]

Marginal cost per 1 hamburger =12. Demand per hour is P=30-0,1Q. What is the price that maximizes profit of a restaurant?

[ArcSine]

There is a shortcut to the answer, given by the relationships between the functions and their first derivatives. But it's insightful to build up from the ground to see the individual parts in action.

You're given Price P as a function of Quantity Q. From there, determine your Revenue function (also as a fctn of Q), which is just P x Q.

You're also given Cost as a function of Q, and so the profit function is Total Revenue less Total Cost, or

R(Q) - C(Q)

You'll see that the profit function is a convex-down quadratic, meaning that it has a single extremum, and further, it's a maximum. Thus the value of Q at which the first derivative of the profit function = zero gives the output at which profit is maximized.

Here's where you take over and show your effort.