# SOLUTION: 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 d

Algebra ->  Functions -> SOLUTION: 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 d      Log On

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 Algebra: Functions, Domain, NOT graphing Solvers Lessons Answers archive Quiz In Depth

 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?Answer by ankor@dixie-net.com(16524)   (Show Source): 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? : 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, : a = +1/2; b=-10; c=80 (but is not used here) : The vertex formula: n = -b/(2a) : n = -(-10) / 2(1/2) : n = +10/1 : n = 10 is the number of employees required for minimum cost. : Find the cost by substituting 10 for n in the equation: P(10) = (1/2)10^2 - 10(10) + 80 : p(10) = 50 - 100 + 80 : P(10) = 30 dollars is the minimum cost