Bus Econ 2.2.49 Let C(x) be the cost to produce x batches of widgets, and let R(

Question

Bus Econ 2.2.49 Let C(x) be the cost to produce x batches of widgets, and let R(x) be the revenue in thousands of dollars. Complete parts (a) through (d) below R(x)=-x2+8x. C(x)=x+10 Using the expressions -x2 8x and/or x 10, identify an equation to be solved in order to find the minimum break-even quantity 24. Simplify your answer.) (c) Find the maximum revenue. How can the maximum revenue be found? Choose the correct answer below 12 16 20 A. Find the y-coordinate of the vertex of Rx). O B. Find the y-intercept of Rx). Find the x-coordinate of the vertex of R(x). Find the maximum y-coordinate of a point where R(x)-c(x). C. D. The maximum revenue isdollars)

Explanation / Answer

At break even,

C(x)=R(x)

-x² +8x =x+10

x² -7x +10 =0

(x-5) (x-2) =0

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hence

x =2, 5

Thus, minimum quantity is 2

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R(x) =-x²+8x

= -(x² -8x)

=-(x² -8x +16) +16

= -(x-4)² +16

Thus, vertex is at (4, 16)

Hence, y coordinate of vertex is 16.

Hence maximum revenue is 16 thousand dollars = 16000 dollars

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