SOLUTION: A caterer in quoting the charge for producing a dinner proposes the following terms. For a group of 60 people, he will charge $30 per person. For every extra 10 people, he will low

Question 536681: A caterer in quoting the charge for producing a dinner proposes the following terms. For a group of 60 people, he will charge $30 per person. For every extra 10 people, he will lower the price for $1.50 per person for the whole group. What size group does the caterer want to maximize his income?
Thanks!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A caterer in quoting the charge for producing a dinner proposes the following terms.
For a group of 60 people, he will charge $30 per person.
For every extra 10 people, he will lower the price for $1.50 per person for the whole group.
What size group does the caterer want to maximize his income?
:
Let x = no. of groups of 10, that will maximize income
Let x = no. of $1.50 reductions in price
Let R = his income
;
R = (60+10x)(30 - 1.50x)
FOIL
R(x) = 1800 - 90x + 300x - 15x^2
R(x) = -15x^2 + 210x + 1800
Find the axis of symmetry
x =
x =
x = +7 groups of 10, 70 more people which would be 130 total
:
Cost per person then, 30 - 7(1.50) = $19.50
:
Total income: 19.50 * 130 = $2,535
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