Suppose a company's revenue function is given by $\displaystyle {R}{\left({q}\right)}=-{q}^{{3}}+{330}{q}^{{2}}$ and its cost function is given by $\displaystyle {C}{\left({q}\right)}={130}+{18}{q}$, where $\displaystyle {q}$ is hundreds of units sold/produced, while $\displaystyle {R}{\left({q}\right)}$ and $\displaystyle {C}{\left({q}\right)}$ are in total dollars of revenue and cost, respectively.

A) Find a simplified experssion for the profit function

$\displaystyle \pi{\left({q}\right)}=$ Preview Question 6 Part 1 of 3  

B) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.)

$\displaystyle {M}{P}{\left({q}\right)}=$ Preview Question 6 Part 2 of 3  

C) How many items (in hundreds) need to be sold to maximize profits? (Round your answer to two decimal places.)

Answer: hundred units must be sold.