Average and marginal cost Consider the following cost functions. a

dictetzqh

dictetzqh

Answered question

2021-11-20

Average and marginal cost Consider the following cost functions.
a. Find the average cost and marginal cost functions.
b. Determine the average cost and the marginal cost when x=a.
c. Interpret the values obtained in part (b). C(x)=0.04×2+100x+800,0x1000,a=500

Answer & Explanation

Twereen

Twereen

Beginner2021-11-21Added 13 answers

Step 1 Given
C(x)=0.04×2+100x+800,0x1000,a=500
a) Find average cost
Average cost a(x)=c(x)x
a(x)=0.04x2+100x+800x
Marginal cost function =a(x)
a(x)=ddx(0.04x2+100x+800x)
Apply the quotient rule here and find the derivative
(fg)=fggfg2
=x(2(0.04x)+100)1(0.04x2+100x+800)x2
=0.08x2+100x+0.04x2100x800x2
=0.04x2800x2
Step 2 The average cost and the marginal cost when x=a
a(x)=0.04x2+100x+800x
Now a=500 plug in a(x)
a(500)=0.04(500)2+(500)+800500
=0.04(250,000)+50,000+800500
=40800500
a(500)=81.6
Now we need to find a'(500)
a(500)=(0.04(500)28005002)
=0.04(250,000)800250,000
=10,800250,000
a(500)=0.0432
c) marginal cost decreases

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