Posted by **jenn** on Monday, February 23, 2009 at 5:39pm.

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

- math -
**Reiny**, Monday, February 23, 2009 at 5:55pm
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

- math -
**Damon**, Monday, February 23, 2009 at 5:55pm
.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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