crappy word problem

[flamathdummy]

It costs Acme Manufacturing C dollars per hour to operated its golf ball division. An analyst has determined that C is related to the number of golf balls produced per hour, x, by the equation C =0.009x^2 - 1.8x +100. What number of balls per hour should Acme produce to minimize the cost per hour of manufacturing these golf balls?

I am confused on where to even start

 

[tkhunny]

C =0.009x^2 - 1.8x +100 -- minimize

You should just have read a section on quadratic equations, maybe parabolas. This section should have told you that the minimum or maximum is equidistant from the zeroes and on the Real axis. The section may have presented a few ways to find the middle.

1) Complete the Square: A(x-B)^2 - C and just read the number C.
2) Factor to find the zeroes, if they are real and rational. Then average them.
3) Use the quadratic formula to find the roots, no matter what they are, then average them.
4) Use method 3 to figure out that the equation is talking to you. If the equation is Ax^2 + Bx + C, the answer is x = -B/(2*A).

Whoops, I'm writing a textbook.

 

[soroban]

Hello, flamathdummy!

It costs Acme Manufacturing C dollars per hour to operated its golf ball division.
An analyst has determined that C is related to the number of golf balls produced per hour, x,
by the equation: C = 0.009x^2 - 1.8x + 100.

What number of balls/hour should Acme produce to minimize the cost/hour of manufacturing these golf balls?

If you're not in a Calculus course, you should be familiar with parabolas.

The cost function is a parabola, opening upward.
. . . Hence, it has a minimum point (where it "bottoms out").
This happens at the vertex.
. . . The vertex is found at: . x .= .(-b)/(2a)

In this problem: . a = 0.009, .b = -1.8
. . . Hence: . x .= .-(-1.8)/(2)(0.009) .= .100

Therefore, Acme should produce 100 golf balls per hour to minimize cost.

 

[flamathdummy]

We are starting parabolas this week and it has really thrown me for a loop. Thanks for the assistance...I was pretty sure that I had to minimize first.