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) = 0.5x^2-130x+17,555. What is the minimum unit cost?

The minimum cost is $9,105

Step-by-step explanation:

To find the minimum cost differentiate the equation of the cost and equate the answer by 0 to find the value of x which gives the minimum cost, then substitute the value of x in the equation of the cost to find it

∵ C (x) = 0.5x² - 130x + 17,555

- Differentiate it with respect to x

∴ C' (x) = (0.5) (2) x - 130 (1) + 0

∴ C' (x) = x - 130

Equate C' by 0 to find x

∵ x - 130 = 0

- Add 130 to both sides

∴ x = 130

∴ The minimum cost is at x = 130

Substitute the value of x in C (x) to find the minimum unit cost

∵ C (130) = 0.5 (130) ² - 130 (130) + 17,555

∴ C (130) = 9,105

∵ C (130) is the minimum cost

∴ The minimum cost is $9,105