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 (i

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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?
Answer by funmath(2873) About Me  (Show Source):
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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%28x=-b%2F2a%29
Your quadratic equation is in standard formhighlight%28f%28x%29=ax%5E2%2Bbx%2Bc%29, a=(1/2), b=-10, and c=80, so
x=-%28-10%29%2F%282%281%2F2%29%29
x=10%2F1
highlight%28x=10%29 This is the amount of employees and guests that produce the minimum cost, 10.
Find P(10) to find the minimum cost:
P%2810%29=%281%2F2%29%2810%29%5E2-10%2810%29%2B80
P%2810%29=%281%2F2%29%28100%29-100%2B80
P%2810%29=50-100%2B80
highlight%28P%2810%29=30%29 The minimum cost is $30.
Happy Calculating!!!