The cost function for a product is C(x)=0.8x^2 +120x+110.
How to find average cost over [0,600] ?

Question

William Abdalla · Accepted Answer

#C_(avg)=barC=1/600int_0^600C(x)dx=132110#

The average price during this time frame can be found by

#C_(avg)=1/(600-0)int_0^600C(x)dx#

#=1/600int_0^600 (0.8x^2+120x+110)dx#

#=1/600 [ (0.8x^3)/3+(120x^2)/2+110x]_0^600#

#=1/600[57600000+21600000+66000-0]#

#=132110#.

Isaiah Allen · Answer

undefined To find the average cost over the interval [0, 600], you need to divide the total cost by the total quantity produced over that interval. The total cost is the integral of the cost function C(x) over the interval [0, 600], and the total quantity produced is 600 units.

First, find the integral of the cost function C(x) over the interval [0, 600]:

∫[0,600] C(x) dx = ∫[0,600] (0.8x^2 + 120x + 110) dx

Then, evaluate this integral:

∫[0,600] (0.8x^2 + 120x + 110) dx = [0.8*(1/3)*x^3 + 120*(1/2)*x^2 + 110*x] evaluated from x = 0 to x = 600

= 0.8*(1/3)*600^3 + 120*(1/2)*600^2 + 110*600 - 0.8*(1/3)*0^3 - 120*(1/2)*0^2 - 110*0

= (0.8*(1/3)*600^3 + 120*(1/2)*600^2 + 110*600)

Then, divide the total cost by the total quantity produced:

Average Cost = Total Cost / Total Quantity Produced

= [(0.8*(1/3)*600^3 + 120*(1/2)*600^2 + 110*600)] / 600

The cost function for a product is C(x)=0.8x^2 +120x+110. How to find average cost over [0,600] ?

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