Question 515787
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 = {{{(-22)/(2*-1)}}} 
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