Question

When no more than 110 units are​ produced, the cost of producing y units is given by​ c(x). ​c(x)equals0.2 x cubed minus 24 x squared plus 1524 x plus 31 comma 272 how many units should be produced in order to have the lowest possible average​ cost?

Answer 1

Given that the cost of production is modeled by:
c(x)=0.2x^3-24x^2+1524x+31272
for lowest average cost, we calculate c'(x)=0
thus:
From c(x), we shall have:
c'(x)=0.6x^2-48x+1524
solving for x we get:
x=40+/- 30.6594i
but since we are looking for a definite number of units, we shall do away with the complex part such that we shall remain with:
x=40 units
hence the minimum number of units will be 40 units