Question

A manufacturer of widgets finds that the production cost, C, in dollars per unit is a function of the number of widgets produced. The selling price, S, of each widget in dollars is a function of the production cost per unit.

C(x) = –0.1x2 + 100


S(C) = 1.4C



What is the selling price per widget as a function of the number of widgets produced, and what should the selling price be if 15 widgets are produced?


A.C(S(x)) = –0.196x^2 + 100; $108.64

B.C(S(x)) = –0.196x^2 + 100; $55.90

C.S(C(x)) = –0.14x^2 + 140; $144.41

D.S(C(x)) = –0.14x^2 + 140; $108.50


This is a question on composite functions.

Answer 1

D

Explanation:

The value of the function at 870, the local maximum, is

= -0.02(870)2 + 34.80(870) - 4700

= -0.02(756900) + 30276 - 4700

= -15138 + 25576

= 10438

So the vertex is (870, 10438)

The cost t the company to produce 870 widgets is

C(870) = 4700 + 5.20(870) = 4700 + 4524 = 9224

So, the cost of the widgets plus the profit must be equal to the total sales, which is divided by the number of widgets reveal their individual price.

(10438 + 9224)/870 = 19662/870 = $22.60

P(x) = 7700

- 0.02x2 + 34.80x - 4700 = 7700

-0.02x2 + 34.80x -12400 = 0

x = {-34.80 ± √[(34.80)2 - 4(-0.02)(-12400)]}/2(-0.02)

x = [-34.80 ± √(1211.04 - 992)]/(-0.04)

x = (-34.80 ± √219.04)/(-0.04)

x = (-34.80 ± 14.8)/(-0.04)

x = 870 ± 370

so, $7700 in profits will be earned at either 500 widgets or 1240 widgets

Answer 2

S(C(x)) = –0.14x2 + 140; $108.50 - On edgenuity the answer is D.

Explanation: