Maximizing revenue A sales analyst determines that the

Chapter 7, Problem 44E

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QUESTION:

Maximizing revenue A sales analyst determines that the revenue from sales of fruit smoothies is given by \(R(x)=-60 x^{2}+300 x\), where x is the price in dollars charged per item, with \(0 \leq x \leq 5\).

a. Find the critical points of the revenue function.

b. Determine the absolute maximum value of the revenue function and give the price that maximizes the revenue.

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QUESTION:

Maximizing revenue A sales analyst determines that the revenue from sales of fruit smoothies is given by \(R(x)=-60 x^{2}+300 x\), where x is the price in dollars charged per item, with \(0 \leq x \leq 5\).

a. Find the critical points of the revenue function.

b. Determine the absolute maximum value of the revenue function and give the price that maximizes the revenue.

ANSWER:

STEP_BY_STEP SOLUTION Step-1 Let f be a continuous function defined on an open interval containing a 1 number ‘c’.The number ‘c’ is critical value ( or critical number ). If f (c) 1 = 0 or f (c) is undefined. A critical point on that graph of f has the form (c,f(c)). Step-2 When an output value of a function is a maximum or a minimum over the entire domain of the function, the value is called the absolute maximum or the absolute minimum. Let f be a func tion with domain D and let c be a fixed constant in D . Then the output value f( ) is the 1. Absolute maximum value of f on D if and only if f(x) f(c) , for all x in D. 2. Absolute minimum value of f on D if and only if f(c) f(x) , for all x in D. Step_3 a) .Given is ; A sales analyst determines that the revenue from sales of fruits 2 smoothies is R(x) = -60x + 300x , here x is the price in dollars charged per item , with 0 x 5. Now , we have to find the critical p

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