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the marginal revenue for x items in dollars is given by R'(x)=-2x+12 determine (a) the...

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the marginal revenue for x items in dollars is given by R'(x)=-2x+12 determine (a) the revenue function and b)the demand function

a)the revenue function is given by R(x)=

b)the demand function is given by p=

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Given the marginal revenue, you can get the revenue by taking the integral of R'(x).

R'(x)= -2x + 12

So,

`a)int R'(x) = int (-2x + 12)`

You may apply the Power Formula: `int u^n = (u^(n+1))/(n+1)`

The Revenue is:

`R(x) = (-2*x^(1+1))/(1+1) + (12*x^(0+1))/(0+1)` 

`R(x) = -(2x^2)/2 + 12x`

`R(x) = -x^2 + 12x`

For the second question, recall that revenue = x * q.

where qis the quantity demand and x is the unit price.

So to get the demand function, factor out x.

`b) -x^2 + 12 x = x(-x + 12)`

There for the demand function, q is `-x + 12.`

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