### Revenue, Cost, and ProfitThe total cost and the total revenue (in dollars) for the production and sale of $ x $ hair dryers are given, respectively, by:\[ C(x) = 5x + 2,340 \]\[ R(x) = 40x - 0.1x^2 \]for $ 0 \leq x \leq 400 $.#### Tasks:(A) **Find the value of $ x $ where the graph of $ R(x) $ has a horizontal tangent line.**(B) **Find the profit function $ P(x) $.**(C) **Find the value of $ x $ where the graph of $ P(x) $ has a horizontal tangent line.**(D) **Graph $ C(x) $, $ R(x) $, and $ P(x) $ on the same coordinate system for $ 0 \leq x \leq 400 $. Find the break-even points. Find the $ x $-intercepts of the graph of $ P(x) $.**

Name: ### Revenue, Cost, and ProfitThe total cost and the total revenue (in
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Description: ### Revenue, Cost, and ProfitThe total cost and the total revenue (in dollars) for the production and sale of $ x $ hair dryers are given, respectively, by:\[ C(x) = 5x + 2,340 \]\[ R(x) = 40x - 0.1x^2 \]for $ 0 \leq x \leq 400 $.#### Tasks:(A)

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### Revenue, Cost, and Profit

The total cost and the total revenue (in dollars) for the production and sale of $ x $ hair dryers are given, respectively, by:

\[ C(x) = 5x + 2,340 \]

\[ R(x) = 40x - 0.1x^2 \]

for $ 0 \leq x \leq 400 $.

#### Tasks:

(A) **Find the value of $ x $ where the graph of $ R(x) $ has a horizontal tangent line.**

(B) **Find the profit function $ P(x) $.**

(C) **Find the value of $ x $ where the graph of $ P(x) $ has a horizontal tangent line.**

(D) **Graph $ C(x) $, $ R(x) $, and $ P(x) $ on the same coordinate system for $ 0 \leq x \leq 400 $. Find the break-even points. Find the $ x $-intercepts of the graph of $ P(x) $.**

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