How Do You Find Quantities Related to Revenue and Cost?

In this problem, you were given revenue and cost functions like $\displaystyle R(x)=-{{x}^{2}}+8x$ and $\displaystyle C(x)=2x+5$. In the parts of the problem you were asked to a) identify the correct graph, b) find the break-even quantity, c) the maximum revenue, and d) the maximum revenue. In class yesterday, the students worked in groups to solve this problem. Here is the work they put on the board.

Parts a and b

Parts c and d

Look pretty good but on part d, they should write the profit at x = 4 as P(4). The key in thee part is to use $\displaystyle x=-\frac{b}{2a}$ on the quadratic revenue and profit functions to find the quantities at which the maximums are achieved. Since the parts asked you to find the maximum revenue and profit, you need to put the quantities into the functions.