A 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 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 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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topeadeniran2 topeadeniran2 · Answer 2 · 2021-10-12T13:08:25+02:00

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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A 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 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.

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A 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 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.