document.write( "Question 56698: 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? \n" ); document.write( "
Algebra.Com's Answer #38594 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
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?
\n" ); document.write( ":
\n" ); document.write( "P(n) = (1/2)n^2 - 10n + 80 is a quadratic equation, so minimum can be obtained by finding the vertex: In the form an^2 + bn + c,
\n" ); document.write( ":
\n" ); document.write( "a = +1/2; b=-10; c=80 (but is not used here)
\n" ); document.write( ":
\n" ); document.write( "The vertex formula:
\n" ); document.write( "n = -b/(2a)
\n" ); document.write( ":
\n" ); document.write( "n = -(-10) / 2(1/2)
\n" ); document.write( ":
\n" ); document.write( "n = +10/1
\n" ); document.write( ":
\n" ); document.write( "n = 10 is the number of employees required for minimum cost.
\n" ); document.write( ":
\n" ); document.write( "Find the cost by substituting 10 for n in the equation:
\n" ); document.write( "P(10) = (1/2)10^2 - 10(10) + 80
\n" ); document.write( ":
\n" ); document.write( "p(10) = 50 - 100 + 80
\n" ); document.write( ":
\n" ); document.write( "P(10) = 30 dollars is the minimum cost \n" ); document.write( "
\n" );