If C(x) is the cost of producing x units of a commodity, then the average cost p

Question

If C(x) is the cost of producing x units of a commodity, then the average cost per unit is a(x) -Cx)/x. Consider the C(x) given below. Round your answers to the nearest cent x) 81,000+280x6x-3/2 (a) Find the total cost at a production level of 1000 units. (b) Find the average cost at a production level of 1000 units. dollars per unit (c) Find the marginal cost at a production level of 1000 units. dollars per unit (d) Find the production level that will minimize the average cost. units e) what is the minimum average cost? dollars per unit

Explanation / Answer

a. C(x)=81000+280x+6x3/2

C(100)=81000+280(100)+6(100)3/2=10900+6000=169000

b.Average cost=C(x)/x =(81000/x)+280+6x1/2

at x=100

(81000/100)+280+6(100)1/2=810+280+60=1150

c.Marginal cost is the derivative of cost function that is

280+6(3/2)x1/2=280+9x1/2

at x=100

280+9(100)1/2=370

d.First we need to find marginal average cost by differentiating average cost function that is

-(81000/x2)+6(1/2)(1/x1/2)= -(81000/x2)+3/x1/2=0

x=900

e. minimum average cost

(81000/900)+280+6(900)1/2=370+180=550

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