A department store is selling a digital graphics tablet in small quantities. These are the cost and revenue functions associated with the tablets, where x represents the selling price of a single tablet:

R(x) = -0.388x2 + 76x
C(x) = -15.18x + 4,074

To make a profit, between what two values should the store set the selling price?

A.
$40 and $196
B.
$55 and $108
C.
$60 and $175
D.
$75 and $212

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calculista calculista · Answer 1 · 2020-03-29T07:54:54+02:00

Answer:

C. $60 and $175

Step-by-step explanation:

we know that

Te profit is equal to the revenue minus the cost

we have

[tex]R(x)=-0.388x^2+76x[/tex] ----> the revenue

[tex]C)x)=-15.18x+4.074[/tex] ---> the cost

Find the profit P(x)

[tex]P(x)=-0.388x^2+76x-(-15.18x+4.074)[/tex]

[tex]P(x)=-0.388x^2+76x+15.18x-4.074[/tex]

Combine like terms

[tex]P(x)=-0.388x^2+91.18x-4.074[/tex]

This is a vertical parabola open downward

The vertex represent a maximum

The x-intercepts represent the values of x when the value of P is equal to zero

That means

The interval between the two roots are the two values that the store should price to make a profit

using a graphing tool

Find out the x-intercepts

The x-intercepts are (60,0) and (175,0)

see the attached figure

therefore

Option C