word problem

Question

Sergio is in the R.O.T.C. at his local high school and needs to raise money for a trip to see the Blue Angels perform. Sergio and his fellow students decide to make and sell their version of Silly Bandz made out of pipe cleaners that represent their school colors. The cost of their business is given by the function
C(x) = 0.5(x − 30)2 + 90 dollars, where x ≥ 0 is the number of Silly Bandz sold.


(a) Find the vertex of the cost function.

(x, C(x)) =


(b) How many Silly Bandz must they sell to minimize their costs?


(c) State the minimum total cost.


(e) Find the increasing and decreasing intervals. (Enter your answer using interval notation.)

Answer 1

Hi.

 

(a) Consider the vertex form a(x-h)²+k, where (h,k) is the vertex. In other words, re-write your cost function in this form. You don't need to do much since your cost function is already in this form.

 

(b) The key in this problem is the word "minimize." Graph your cost function and see what is your minimum point. Make sure you label your x-axis and y-axis. That should give you a sense of how to answer this question.

 

(c) Refer to (b).