Question

IncorrectYour answer is incorrectA vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then theunit cost is given by the function C()0.3x-66x + 13,267. What is the minimum unit cost?Do not round your answer.Unit cost: S1dxCheckSave For LaterSubmit AssignmentPrencyAceeshhy1125 PMWednesday1620212021 MMcGraw-H Education, All Riathts Resered.Torms of Use9Type here to search

Answer 1

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.