A math question please help me.?

Question

Sally produces cell phones. She estimates that by selling them for x dollars each, she will be able to sell 265-2x each week. Determine what price will yield a maximum revenue.

troslim · Answer

Revenue=price*quantity=x*(265-2x)=265x-2x^2
Derivative=265-4x
265-4x=0 --> 265=4x
x=66,25
Price=66,25 , revenue=17490

pruthakp9 · Answer

to determine the price that will yield maximum revenue for sally's cell phones, we need to analyze the revenue function based on the selling price

x

per phone. the number of phones sold per week is given by the function

q (x) = 265 - 2 x

, where

x

is the selling price in dollars. the revenue

r

generated per week can be calculated as:

r (x) = x \times q (x)

r (x) = x \times (265 - 2 x)

r (x) = 265 x - 2 xsqr2

now, to find the price

x

that maximizes revenue

r (x)

, we will use calculus by finding the critical points of the revenue function

r (x)

and determining whether they correspond to a maximum.

r (x) = 265 x - 2 x^{2,}

r^{'} (x) = \frac{d}{dx} [265 x - 2 x^{2}]

r^{'} (x) = 265 - 4 x

r^{'} (x) = 0

265 - 4 x = 0

4 x = 265

x = 265

x = 66.25

x = 66.25

r^{''} (x) =d/dx [265 - 4 x]

r^{''} (x) = - 4

r^{''} (x) = - 4

x = 66.25

therefore, the price that will yield maximum revenue for sally's cell phones is

66.25

dollars per phone. this means that by selling each phone for $66.25, sally will maximize her weekly revenue based on the estimated sales function

q (x) = 265 - 2 x

.

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A math question please help me.?

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