SOLUTION: search the seas cruise ship has a conference room offering unlimited internet access that can hold up to 60 people. companies can reserve the room for groups of 38 or more. if the

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Question 515787: search the seas cruise ship has a conference room offering unlimited internet access that can hold up to 60 people. companies can reserve the room for groups of 38 or more. if the group contains 38 people, the company pays $60 per person. the cost per person is reduced by $1 for each person in excess of 38. find the size of the group that maximizes the income for the owners of the ship, and determine the income.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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can hold up to 60 people. companies can reserve the room for groups of 38 or more. if the group contains 38 people, the company pays $60 per person.
the cost per person is reduced by $1 for each person in excess of 38.
find the size of the group that maximizes the income for the owners of the ship, and determine the income.
:
let x = no. of men in the group
Also x = no. of one dollar reductions
:
f(x) = income for the ship
:
Income = no. * cost
f(x) = (38+x)(60-x)
FOIL
f(x) = 2280 - 38x + 60x - x^2
A quadratic equation
f(x) = -x^2 + 22x + 2280
The max occurs on the axis of symmetry, x = -b/(2a)
x = %28-22%29%2F%282%2A-1%29
x = +11 men over 38 for max income
:
A group of 11+38 = 49 will give max income
:
Find the income
49(60-11) = $2401