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(x1.25)^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
(x1.25)^2 = 3.57 (y  .562)
so I get vertex at (1.25 , .562)
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