8. Suppose that to make n sunglasses, it costs a company f(n) dollars, where f(n

Question

8. Suppose that to make n sunglasses, it costs a company f(n) dollars, where f(n) 2n+2000. a. What are the fixed costs associated with production of the sunglasses, i.e. what are the costs that the company incurs for setting up to produce the sunglasses, even if they don't actually produce any? Copyright (e) 2013, Edfinity, Inc. Reproduction without Edfinity's permission is strictly forbidden Page 8 of 13 Ceand ing edfinity Set 6 b. Define A(n) to be the function giving the average cost per pair of

Explanation / Answer

Function is : f(n) = n^3 + 2n + 2000


a. .

Fixed cost = f (0) = 0 +0 + 2000 = 2000

b.

Average Cost, A (n)

A(n) = total cost to produce x sunglasses / number of sunglasses
A(n) = f(n) / n
A(n) = n^2 + 2 + 2000/n, n > 0

c.

A'(n) = 2n 2000/n²

2n 2000/n² = 0
2n = 2000/n²
n³ = 1000
n = 10

Number of sunglasses that minimize average cost = 10

Minimum average cost
= A(10) = 10^2 + 2 + 2000/10 = 302

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