document.write( "Question 56702: Assume the cost of a company picnic is described by the function
\n" ); document.write( "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 #38479 by funmath(2933) $\"\"$ $\"About$

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Assume the cost of a company picnic is described by the function
\n" ); document.write( "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( "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 $\"highlight%28x=-b%2F2a%29\"$
\n" ); document.write( "Your quadratic equation is in standard form $\"highlight%28f%28x%29=ax%5E2%2Bbx%2Bc%29\"$ , a=(1/2), b=-10, and c=80, so
\n" ); document.write( " $\"x=-%28-10%29%2F%282%281%2F2%29%29\"$
\n" ); document.write( " $\"x=10%2F1\"$
\n" ); document.write( " $\"highlight%28x=10%29\"$ This is the amount of employees and guests that produce the minimum cost, 10.
\n" ); document.write( "Find P(10) to find the minimum cost:
\n" ); document.write( " $\"P%2810%29=%281%2F2%29%2810%29%5E2-10%2810%29%2B80\"$
\n" ); document.write( " $\"P%2810%29=%281%2F2%29%28100%29-100%2B80\"$
\n" ); document.write( " $\"P%2810%29=50-100%2B80\"$
\n" ); document.write( " $\"highlight%28P%2810%29=30%29\"$ The minimum cost is $30.
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "

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