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Sagot :
Please check that the expression for the cost you typed reflects what you read in the problem.
Isn't there a "square" in one of the "x" values of the cost equation?
Great. I see now the actual equation for cost to be:
Cost = 0.3 x^2 - 66 x + 13267.
The minimum unit cost will be given by the minimum of this quadratic function (a parabola) which has a minimum at the parabola's vertex. Notice this is a parabola with branches pointing UP because the coefficient of the term in x^2 is POSITIVE.
Recall then the equation for the x position of the vertex of a pparabola with equation of the form:
y = a x^2 + b x + c
the x-position of the vertex is: x = - b / (2a)
which in our case gives:
x of the vertex = - (- 66) / (2 * 0.3) = 110
Then, since the x values represent the number of cars that are made , we now that that minimum occurs when the number of cars produced is 110.
We replace this value in the cost equation and get:
Cost = 0.3 (110)^2 - 66 (110) + 13267 = 9637
Then, the unit cost for making the 110 cars is $9637, which is in fact the minimum value we were looking for.
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