Question

Total ProfitA marginal profit function (in dollars per unit) at a production level of units is given byMP(x) = ce-0.6z=where 0 < x < 100.Find the profit for a production level of 100 units.Round your answer to 2 decimal places.

Answer 1

Explanation:

$\begin{gathered} MP(x)=xe^{-0.6x} \\ x\in\lbrack0,100\rbrack \end{gathered}$

We need to find the profit function, so:

$\begin{gathered} P(x)=\int MP(x)=\int xe^{-0.6x}dx \\ so\colon \\ P(x)=\int xe^{-0.6x}dx=-\frac{5}{3}e^{-(\frac{3x}{5})}x-\frac{25}{9}e^{-(\frac{3x}{5})}+C \\ P(0)=\frac{25}{9} \\ C=\frac{25}{9} \end{gathered}$

Therefore:

x = 100

$P(100)\approx2.78$

Answer:

2.78