Chapter 4.2, Problem 28E

In Exercises 1-8, calculate total cost (disregarding any fixed costs) or total profit.

Total profit from marginal profit. Poyse Inc. has a marginal-profit function given by

$P^{\prime }\left(x\right)=-2x+80$,

where $P\text{'}\left(x\right)$

Is in dollars per units. This means that the rate of change of total profit with respect to the number of units produced, x, is $P\text{'}\left(x\right)$. Find the profit from the production and sale of the first 40 units.