# math

the cost per hour of running an assembly line in a manufacturing plant is a function of the number of items produced per hour. The cost function is C(x) = 0.28x^2 - 0.7x + 1 where C(x) is the cost per hour in thousands of dollars and x is the number of items produced per hour in thousands. Determine the most economical production level.... i tried completing the square but i don't seem to get the right answer... please help

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1. completing the square:
C(x) = 0.28x^2 - 0.7x + 1
= .28[x^2 - 2.5x + .......] + 1
= .28[x^2 - 2.5x + 1.5625 - 1.5625] + 1
=
=
= .28(x-1.25)^2 + .5625

take it from there, remember x is in thousands

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2. .28 x^2 - .7 x + 1 = y
divide both sides by .28
x^2 - 2.5 x + 3.57 = 3.57 y
x^2 - 2.5 x = 3.57 y -3.57
add 1.25^2 = 1.56 to both sides
x^2 - 2.5 x +1.56 = 3.57 y - 2.00
(x-1.25)^2 = 3.57 (y - .562)
so I get vertex at (1.25 , .562)

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