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The management of Ditton Industries has determined that the daily marginal revenue function associated with selling x units of their deluxe toaster ovens is given by the following, where R '(x) is measured in dollars/unit.R'(x)= -0.1x+40(a) Find the daily total revenue realized from the sale of 230 units of the toaster oven.(b) Find the additional revenue realized when the production (and sales) level is increased from 230 to 330 units.

Respuesta :

Edufirst

Answer:

  • a) 6,555 dollars

  • b) 1,200 dollars

Explanation:

The marginal revenue is the derivative of total revenue with respect to demand:

           [tex]R'=\dfrac{dR(x)}{dx}[/tex]

You are given the function R' and need to find the function R, which you can do by integrateing from 0 to R:

         [tex]R'(x)= -0.1x+40\\\\\\\dfrac{dR(x)}{dx}=-0.1x+40\\\\\\dR(x)=(-0.1x+40)dx\\\\\\\int\limits^{R(x)}_0 {dR(x)}=\int\limits^x_0 {(-0.1x+40)} \, dx \\\\\\R(x)=-0.1x^2/2+40x\\\\\\R(x)=-0.05x^2+40x[/tex]

(a) Find the daily total revenue realized from the sale of 230 units of the toaster oven.

Substitute with x = 230

      [tex]R(230)=-0.05(230)^2+40(230)=-2,645+9,200=6,555[/tex]   (dollars)

(b) Find the additional revenue realized when the production (and sales) level is increased from 230 to 330 units.

You must find R(330) - R(230)

Since we already calcualted R(230), goe with R(330):

       [tex]R(330)=-0.05(330)^2+40(330)=-5,445+13,200=7,755[/tex]  (dollars)

       [tex]R(330)-R(230)=7,755-6,555=1,200[/tex]  (dollars)

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