Question

The cost C in dollars of manufacturing x bicycles at a production plant is given by the function shown below.

C(x) = 5x²-1500x + 125,000
a. Find the number of bicycles that must be manufactured to minimize the cost.
b. Find the minimum cost.
a. How many bicycles must be manufactured to minimize the cost?
bicycles

Answer 1

Given function:

• C(x) = 5x² - 1500x + 125000

It has a positive leading coefficient, hence the parabola opens up. It means it has the minimum point at vertex.

The x-coordinate of the vertex is:

• x = - b/(2a) = - (-1500)/(2*5) = 150

The minimum cost is:

• C(150) = 5(150)² - 1500(150) + 125000 = 12500

Answer:

• a) The minimum number of bicycles is the x-coordinate of the vertex, 150,
• b) The minimum cost is the value of C when x is 150, this is $12500.