Chapter 2.6, Problem 2E

Marginal revenue, cost, and profit, Let $R\left(x\right),C\left(x\right),\text{and}P\left(x\right)$ be, respectively, the revenue cost and profit in dollars from the production and sale of x items If

$R\left(x\right)=5x\text{and}C\left(x\right)=0.001x^2+1.2x+60,$

Find each of the following

a. $P\left(x\right)$

b. $R\left(100\right),C\left(100\right),\text{and}P\left(100\right)$

c. $R\text{'}\left(x\right),C\text{'}\left(x\right),\text{and}P\text{'}\left(x\right)$

d. $R\text{'}\left(100\right),C\text{'}\left(100\right),\text{and}P\text{'}\left(100\right)$

e. Describe what each quantity in parts (b) and (d) represents