Problem
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
Solution
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: \(x=\boxed{56}\)
