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

Step-by-step 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=-(5)/(3)e^{-((3x)/(5))}x-(25)/(9)e^{-((3x)/(5))}+C \\ P(0)=(25)/(9) \\ C=(25)/(9) \end{gathered}`

Therefore:

x = 100

`P(100)\approx2.78`

Answer:

2.78