Algebra Problem Please Help!!!!?

Question

The cost C in dollars of manufacturing x bicycles at holidays Production Plant is given by the function c(x) = 2x^2 - 800x +92,000.

Find the number of bicycles that must be manufactured to minimize the cost and find the minimum cost.

Thank You So much!!

Answer 1

This is called an optimization problem, because the answer is actually the vertex of the parabola. So, to find the coordinates of the vertex, you have to complete the square.



c(x) = 2x^2 - 800x + 92000

c(x) = 2(x^2 - 400x) + 92000

c(x) = 2(x^2 - 400x + 40000 - 40000) + 92000

c(x) = 2(x^2 - 400x + 40000) + 12000

c(x) = 2(x - 200)^2 + 12000



The x coordinate of the vertex in this form the parabola is h, where f(x) = a(x - h)^2 + k. The k value is the y coordinate.



So, the number of bicycles that must be manufactured are 200, and the minimum cost is $12000 dollars.

Hope this helps.

Answer 2

This is a minimization problem. You can solve it by:



1. Finding the critical values by setting c'(x) = 0 annd solving for x.

2. Making sure that the critical values are local minimums by making sure that c''(x) is positive at those points.

3. Comparing the values of c(x) at the boundaries with those at the local minimums found from parts 1 and 2.

Answer 3

i m so sorry i m not good in math either