SOLUTION: A motel advertises that it will provide dinner, dancing, and drinks for $60 per couple at a New Year's Eve party. It must have a guarantee of 50 couples. Furthermore, it will agree

Question 666312: A motel advertises that it will provide dinner, dancing, and drinks for $60 per couple at a New Year's Eve party. It must have a guarantee of 50 couples. Furthermore, it will agree that for each couple in excess of 50, it will reduce the price per couple for all attending by $0.25. How many couples will it take to maximize the motel's revenue?

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A motel advertises that it will provide dinner, dancing, and drinks for $60 per couple at a New Year's Eve party. It must have a guarantee of 50 couples. Furthermore, it will agree that for each couple in excess of 50, it will reduce the price per couple for all attending by $0.25. How many couples will it take to maximize the motel's revenue?
**
let x=number of couples to maximize motel's revenue
x-50=number of couples in excess of 50
.25(x-50)=reduction in price per couple
Price per couple=[60-.25(x-50)]
Revenue=number of couples*price per couple
y=x[60-(.25(x-50)]
=x[60-.25x+12.5]
=x[-.25x+72.5]
=-.25x^2+72.5x
complete the square
y=-.25(x^2-290+145^2)+.25*145^2
y=-.25(x-145)^2+5256.25
This is a parabola that opens downwards with a maximum of 5256.25 at x=145
How many couples will it take to maximize the motel's revenue=145

RELATED QUESTIONS
an outdoor adventure company advertises that they will, provide a guided mountain bike... (answered by ankor@dixie-net.com)

A dinner dance is attended by 12 married couples. In how many ways may a dancing couple... (answered by stanbon)

You are traveling to your aunt's house 200 miles away for a surprise birthday party. The... (answered by josgarithmetic,ikleyn,MathTherapy)

1. Wen Seng operates an ice cream shop. He is trying to decide whether to expand his... (answered by ikleyn)

The 2015 senior class from puma high school raised funds for an end of the year party at... (answered by ikleyn)

Party city will provide and deliver balloons for rasheed's birthday party for 10$ plus 50 (answered by lwsshak3)

stephanie is planning her sweet 16 and wants to have live music and food for everyone who (answered by robertb)

A person wishes to deposit $5,000 per year in a savings account which earns interest of 8 (answered by ikleyn)

a restaurant offers 10 entrees. if a party of 6 arrives for dinner, whats the probability (answered by richard1234,sudhanshu_kmr)