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?

Question

Kyan Merritt

Mathematics

16 September, 13:32

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?

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Tyson · 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