1. The marginal average cost of producing x sports watches is given by the 1st d

Question

1. The marginal average cost of producing x sports watches is given by the 1st derivate of the average cost function

barC'(x)=-1000/x^2 and barC(100)=25 where barC(x) is the average cost in dollars.

a) Find the average cost function

b) Find the total cost function

c) What are the fixed costs

2. The demand for a certain type of auto tire is given by x=f(p)=50(1+e^-p/60) where price p is in dollars per tire and x is quantity demanded per week in units of a thousand.

a) If the weekly quantity demanded is 60000 tires find the price per tire

b) If the current price is $120 per tire and is increasing at a rate of $2 per week, what is the rate of change of the demand per week

Please show work in detail so I can follow all of the steps. Thank you in advance for your help.

Explanation / Answer

1> C'(x) = -1000/x^2

C(x) - C(100) = 1000/x - 10

C(x) = 1000/x + 15

total cost TC(x) = 1000 ln(x) + 15x

Fixed cost = 15x

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