Avehicle 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 the unit cost is given by the function c(x)=1.1x^2-660x+107,357. how many cars must be made to minimize the unit cost?
do not round your answer.

The number of cars that must be made to minimize the unit cost is 300 cars.

Since we have been given the cost function to be function c(x)=1.1x² - 660x + 107,357, then we have to find the first differentiation in order to get the value and this will be:

c(x)=1.1x² - 660x + 107,357

2.2x - 660 = 0

Collect like terms

2.2x = 0 + 660

2.2x = 660

x = 660/2.2

x = 300

Therefore, the number of cars that must be made to minimize the unit cost is 300 cars.

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300

Step-by-step explanation:

The vertex of quadratic ax^2 +bx+c is on the line x=-b/(2a). This unit cost function defines a parabola opening upward, so its vertex is its minimum. The location of the vertex is ...

x = -(-660)/(2·1.1) = 660/2.2 = 300

300 cars must be made to minimize the unit cost.

Note:

The unit cost at that production level will be $8357.

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