Question 56702
Assume the cost of a company picnic is described by the function 
P(n)=(1/2)n^2-10n+80  where n represents the number of employees and family members attending the picnic and P (in dollars) represents the cost of the picnic  How many employees and guests in attendance produce a minimum cost?  What is the minimum cost for this event?
The vertex of this parabola gives you the answers that you're looking for.  You find the x value of the parabola with the formula {{{highlight(x=-b/2a)}}}
Your quadratic equation is in standard form{{{highlight(f(x)=ax^2+bx+c)}}}, a=(1/2), b=-10, and c=80, so
{{{x=-(-10)/(2(1/2))}}}
{{{x=10/1}}}
{{{highlight(x=10)}}} This is the amount of employees and guests that produce the minimum cost, 10.
Find P(10) to find the minimum cost:
{{{P(10)=(1/2)(10)^2-10(10)+80}}}
{{{P(10)=(1/2)(100)-100+80}}}
{{{P(10)=50-100+80}}}
{{{highlight(P(10)=30)}}} The minimum cost is $30.
Happy Calculating!!!