Question

Aki's Bicycle Design has determined that when x hundred bicycles are built, the average cost per bicycle =0.9x^2-1.7x+10.861, when C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?

C(x)=0.9x^2-1.7x+10.861 =
C(x)=0.9(x^2-1.889x)+10.861=

My question is how do they come up with the 1.889 in the equation?

For Further Reading

* algebra - drwls, Thursday, March 6, 2008 at 4:44am

They are using the method of "completing the square" and may be trying to get a perfect square inside the parentheses.
-0.9 x 1.88888... and -1.7 are the same thing. They rounded off the the 1.88888.. to 1.889.

With a complete square inside parentheses, C(x) becomes
0.9(x^2 - 1.889x + 0.8920) + 10.861 - 0.8028
= 0.9(x- 0.9445)^2 + 10.058

You get minimum average cost when x = .9445

Okay, that makes sense, but now where do you get the 0.8920 in the equation from?

Answer 1

If you understand the subject of completing the square, you should know that the constant term has to be the square of half of the coefficient of x,
(1.889/2)^2. So, that constant had to be added inside the parentheses and subtracted somewhere else (after being multipled by 0.9)

Answer 2

Thank you very much. I am not very good at Algebra, but maintaining an "A". I want to totally understand how the numbers are arrived at and then it makes complete sense.

Answer 3

You are doing the right thing. Once you understand the logic of each step, it becomes easier to do them yourself. Otherwise, it's like watching rabbits pulled out of a hat in a magic show.