Company ducky finds that in order to sell \"x\" specialty hobbas, the price per

Question

Company ducky finds that in order to sell "x" specialty hobbas, the price per hobba must be p=40x2-2x3-100x+4000    and the cost function is c(x)=1000x+2000

find the total revenue

find the total profit

find how many hobbas the company must produce and sell to have maximum profit

what price per single hobba must be charged in order to have maximum profit?

CAN YOU PLEASE SHOW HOW YOU GET X=15 FROM -8 (x^3-15 x^2+25 x-375) = 0

FROM THE BELOW PROBLEM

Total Revenue is just number of hobbas * price

= x*(40x^2 - 2x^3-100x+4000)

Total profit is just revenue minus cost
= x*(40x^2 - 2x^3-100x+4000) - (1000x+2000)

^^^^We want to maximize the profit function
d/dx(x (40 x^2-2 x^3-100 x+4000)-(1000 x+2000)) = -8 (x^3-15 x^2+25 x-375)
-8 (x^3-15 x^2+25 x-375) = 0
x = 15

At x = 15, the profit function produces 54250


So the company should sell 15 hobbas.

The price per hobba should be
Price = (40x^2 - 2x^3-100x+4000)
Price (15) = 4,750

Explanation / Answer

-8 (x^3-15 x^2+25 x-375) = 0

x^3-15 x^2+25 x-375 = 0

(x^3-15 x^2) + (25 x-375) = 0

x^2 (x - 15) + 25(x - 15) = 0

(x^2 + 25) (x - 15) = 0

Either (x^2 + 25) = 0 or x - 15 = 0

Since x^2 + 25 can never be zero, we get that x-15 = 0 or x = 15.

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