Question: The demand for Guitar Hero can be modeled by \(p=211-0.002x\) and the cost can be modeled by \(c=30x+1,500,000\) where x is the number of units produced.

a. Write the profit function for Guitar Hero.

b. What is the marginal profit when 80,000 units are sold?

c. What is the marginal profit when 50,000 units are sold?

d. What is the average rate of change of the profit from 50,000 to 80,000 units?

e. Determine the price you would charge for Guitar Hero.