If C(x) is the cost of producing x units of a commodity, then the average cost p
ID: 2883279 • Letter: I
Question
If C(x) is the cost of producing x units of a commodity, then the average cost per unit is a(x) = C(x)/x. Consider the C(x) given below. Round your answers to the nearest cent. C(x) = 2,000 + 150x + 4x^3/2 Find the total cost at a production level of 1000 units. $ 278491.1 Find the average cost at a production level of 1000 units. 278.5 dollars per unit Find the marginal cost at a production level of 1000 units. 339.7 dollars per unit Find the production level that will minimize the average cost. i units What is the minimum average cost? dollars per unitExplanation / Answer
given cost C(x)=2000+150x+4x3/2
average cost a(x)=(C(x))/x
a(x)=(2000+150x+4x3/2)/x
a(x)=(2000/x)+150+4x1/2
a'(x)=(-2000/x2)+0+4(1/2)x-1/2
a'(x)=(-2000/x2)+(2/x1/2)
d)for minimum average cost a'(x)=0, a"(x)>0
(-2000/x2)+(2/x1/2)=0 , a"(x)=(4000/x3)-(1/x3/2)
(2000/x2)=(2/x1/2)
x2/x1/2=2000/2
x3/2=1000
x=100
a"(100)=(4000/1003)-(1/1003/2) =0.003 >0
so production level that minimises the average cost is 100 units
e) minimum average cost =a(100)
minimum average cost =(2000/100)+150+4*1001/2
minimum average cost = 210 dollars per unit