The cost to produce football uniforms for a school can be modeled by C(u) = 1/4 u2 - 25u +3500 where C(u) represents the cost in dollars to produce u football uniforms. a. Find the cost to produce 30 uniforms. b. Find the vertex and describe the meaning c. How many uniforms can a school get with a budget of $1600?

Question

The cost to produce football uniforms for a school can be modeled by C(u) = 1/4 u2 - 25u +3500 where C(u) represents the cost in dollars to produce u football uniforms.  a.	Find the cost to produce 30 uniforms.    b.	Find the vertex and describe the meaning   c.	How many uniforms can a school get with a budget of $1600?

anonymous · Answer

1) replace $u$ by $30$ , that is, compute $$C(30)=\frac{1}{4}\times 30^2-25\times 30+3500$$

anonymous · Answer

2) first coordinate of the vertex of $ax^2+bx+c$ is always $-\frac{b}{2a}$ 
in your example $a=\frac{1}{4},b=-25$. compute $-\frac{-25}{2\times \frac{1}{4}}=25\times 2=50$
to find the second coordinate, find $C(50)$

anonymous · Answer

this tells you that the minimum occurs when they produce 50 uniforms (seems rather unlikely, they really stretch for these word problems, don't they?)

anonymous · Answer

3) set $$\frac{1}{4}u^2-25u+3500=1600$$ and solve for $u$
but there is no real solution , so either there is a typo in the question, or it is a trick question and the answer is "they can't buy any"