Suppose that the marginal revenue for firefighting protective clothes is $\overline{M R}=263-2 x$ and the marginal cost is $\overline{M C}=2.5 x+11$ with a fixed cost of $\$ 270$. Assume $R(0)=0$.
a) How many units will result in a maximum profit?
\[
x=
\]
b) Find the revenue function.
\[
R(x)=
\]
c) Find the cost function.
\[
C(x)=
\]
d) What is the maximum profit (to the nearest dollar)?
The maximum profit is

Answer

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Answer

Final Answer: $x=\boxed{56}$

Steps

Step 1 ：Set the marginal revenue equal to the marginal cost: $263 - 2x = 2.5x + 11$.

Step 2 ：Solve the equation for x to find the number of units that will result in maximum profit: $x = 56$.

Step 3 ：Final Answer: $x=\boxed{56}$