Question 435471: The cost C (in dollars) of manufacturing x chairs at Maya's Furniture Factory is given by the function C(x)=0.6x^2-336x+57,718 . What is the minimum cost of manufacturing chairs?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! The cost C (in dollars) of manufacturing x chairs at Maya's Furniture Factory is given by the function C(x)=0.6x^2-336x+57,718 . What is the minimum cost of manufacturing chairs?
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What we need to do here is change this quadratic equation which represents a parabola which opens upwards into the standard form, y=(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex. The y-value would be the minimum cost in this case. An alternative method is the use the formula, x=-b/2a, with x being the x coordinate of the vertex. To find the minimum, just plug this x-value into the original equation and solve for C(x). I will do both methods.
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0.6x^2-336x+57,718
completing the square, factoring out 0.6)
.6(x^2-560x+57718)
(560/2)^2=78400
.6(x^2-560x+78400)+57718-47040
.6(x-280)^2+10678
ans:
The minimum cost is $10678 when 280 chairs are made.
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Alternate method:
a=.6
b=-336
x=-b/2a=-(-336)/2*.6=336/1.2=280
C(x)=0.6x^2-336x+57,718=.6(280)-336(280)+57718
=47040-94080+57718=10678
In this case the second method might be easier. You should learn both methods, however.
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