I need help with this problem. With the remote learning I am having a hard time understanding the problem. Make sure to answer all parts. Thank you

++++++++++++++++++++++++

The demand for a statisticians services is represented by x^D = 20 p, where x measures visits and p is the per visit price. Her forecasting costs increase more than proportionally with each visit. That is, C(x) = x².

(a) The statistician can easily see willingness to pay. Hence, she can perfectly price-discriminate. Calculate her profit maximizing output (visits), as well as her profits.

(b) Suppose the office where she works makes her charge the same price to everybody. What will that price be if she is the only one offering similar services in the park? How many people will come to see her? What profits will she earn?

(c) Assume that the park hires many other statisticians, who perfectly compete with each other. As a result, the market supply of forecasts is given by x^S = p/2. Calculate the competitive price, the total amount of people that will buy this good. Calculate (and graph) the producers' and the consumers' surplus and compare them with their values in parts (a) and (b).

Note: Treat x as a continuous variable. Although it measures people, we could change the units to thousands, millions, etc.