a monopolist faces the demand function p = 140 − 2q, with p denoting the market price and q denoting the quantity demanded.

there is a fixed cost of 200, the total variable cost function is t v c(q) = 1 3q3 − 10q2 + 188q.

(a) obtain an expression for the profit function f(q), defined for q > 0.

(b) determine the derivative of the profit function.

(c) for what value(s) of q the derivative of the profit function equals to zero? explain your answer carefully

expert answer

a) The profit function is

b) The derivative of the profit function is

c) There are no values for Q where .

Step-by-step explanation:

The Profit function is defined as the difference between Revenue function and Cost function, where the Revenue function is defined as the price times the number of products.

So starting with the revenue we have:

where P is the market price and Q the quantity demanded, using the demand function we can write:

a) Thus the Profit function is

b) We can determine the derivative of the profit function using the result on part a).

c) We can set the profit function equal to 0

Since we cannot factor we will have to use quadratic formula.

where the coefficients are

So we get

Notice that we get a negative number inside the square root if we evaluate it.

Since we get a negative number inside the root, then there are no real values of Q where the derivative of the profit function is equal to 0.

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct

answer: (yeees, you need a poet.)

//blooming serenity//

beautiful in the morning

mysterious at night

wonderous nature souring

with all it's mystical might

the flower that blooms

to the fox that looms

nocturnal creatures

with various features

a blooming flower soon in sight

as a new little hatchling fears to take flight  

afraid to leave it's calming nest,

but dear little bird, mother knows best

as sure as there are stars in the sky,

life is not about who, where what, when or why-

it's the journey that follows

adventures we swallow

of   nature's deep wonders,

natural disasters and storm's thunders.

blooming serenity

life and nature, truly is heavenly.

-kerstien lehman

step-by-step explanation: