Question 466509: Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?
Found 2 solutions by ccs2011, lwsshak3:
Answer by ccs2011(207)   (Show Source):
Answer by lwsshak3(11628)  (Show Source):
You can put this solution on YOUR website! Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost.
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To answer the question, you need an equation like y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex, the values of which gives the number of watches Bob must repair to have the lowest cost.
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C(x) = 4x2-296x+85
completing the square: (factor out 4, then take half of the coefficient of the x-term and square it=(74/2)^2=37^2, then add it in to complete the square.)
C(x)=4(x^2-74x+37^2)+85-4(37^2)
C(x)=4(x-37)^2+85-5476
C(x)=4(x-37)^2-5391
This is a parabola with vertex at (37,-5391)
ans:
Bob must repair 37 watches to have the lowest operating cost
See graph below as a visual check on the answer
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