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
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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(22740) (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
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