Question

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 + 418x + 50,459. What is the minimum unit cost?

a) $10,000
b) $20,000
c) $30,000
d) $40,000

Answer 1

The minimum unit cost is $40,000.

Step-by-step explanation:

To find the minimum unit cost, we need to find the vertex of the quadratic function C(x) = -1.1x^2 + 418x + 50,459. The x-coordinate of the vertex is given by -b/2a, where a=-1.1 and b=418. Plugging in these values gives us x = -418/(2*(-1.1)) = 190.9091. Now we can find the unit cost by plugging this value into the function: C(190.9091) = -1.1(190.9091)^2 + 418(190.9091) + 50,459 = $40,309.09. Therefore, the minimum unit cost is d) $40,000.