Question 1128496
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For the general quadratic equation
f(x) = ax^2 + bx + c
the vertex point is (h,k) where h = -b/(2*a) and k = f(h)
The min cost will occur at the vertex as the vertex is the lowest point when a > 0


Based on that general form above, we see that 
C(x) = 0.3x^2 - 2.7x + 7.475
leads to these three coefficients:
a = 0.3
b = -2.7
c = 7.475


Plug in the values of 'a' and 'b' to find h
h = -b/(2*a)
h = -(-2.7)/(2*0.3)
h = 2.7/0.6
h = 4.5
This is the x coordinate of the vertex


Now plug in x = 4.5 to find the value of k
C(x) = 0.3x^2 - 2.7x + 7.475
C(4.5) = 0.3(4.5)^2 - 2.7(4.5) + 7.475
C(4.5) = 0.3(20.25) - 2.7(4.5) + 7.475
C(4.5) = 6.075 - 12.15 + 7.475
C(4.5) = 1.4
k = C(h) = C(4.5) = 1.4


Therefore, the vertex point is (h,k) = (4.5, 1.4)


The minimum average cost per dulcimer is $__<u><font size=4 color=red>1.40</font></u>__.
The company should build __<u><font size=4 color=red>450</font></u>__dulcimers to achieve the minimum.


note: x is the number of dulcimers built and this number is in hundreds. So x = 4.5 indicates 4.5 hundred or 4.5*100 = 450 units are built.
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