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 theunit cost is given by the function C (x) = 0.6x? - 168x+24,278. What is the minimum unit cost?Do not round your answer.Unit cost:Х5?

Answer 1

The given function is expressed as

C(x) = 0.6x^2 - 168x + 24278

This is a quadratic function. The general form of a quadratic function is expressed as

f(x) = ax^2 + bx + c

By comparing with the given function,

a = 0.6

b = - 168

c = 24278

If it is plotted on a graph, a parabola would be formed. It would open upward since the value of a is greater than zero. Thus, the vertex of the graph would give us the minimum value of x. The formula for determining the minimum value is

x = - b/2a

x = - - 168/2 * 0.6 = 168/1.2

x = 140

To find the minimum unit cost, we would substitute the value of x = 140 into the cost function. it becomes

C(140) = 0.6(140)^2 - 168 * 140 + 24278

C(140) = 11760 - 23520 + 24278

C(140) = 12518

Thus, the minimum unit cost is $12518