algebra

posted by .

can anyone please help me set this problem up, I can do the math but I have tried for hours...
Air fare club offers membership at \$300.00, at least 50 people must join.For every member over 50 their fare will be reduced by \$2 for every member. Due to space limits only 125 passengers will be allowed. how many memberships will maximize the revenue?

• algebra -

current rate = \$300
number of members = 50

let the number of additonal member be n

so actual number of members = n+50
cost per member = 300 - 2n

Revenue = number of members x membership fee
= (n+50)(300 - 2n)
= 300n - 2n^2 + 15000- 100n
= -2n^2 + 200n + 15000
= -2(n^2 - 100n + 2500 - 2500 ) + 15000
= -2( (n-50)^2 - 2500) + 15000
= -2(n-50)^2 + 5000 + 15000
= -2(n-50)^2 + 20000

This is a parabola opening downward with a vertex of (50,20000)

So the maximum of Revenue is \$20,000 when n = 50
So 50 addition to the original 50 should join.

The maximum revenue is obtained when 100 members are in.

check:
at 100 members cost is 300 - 2(50) = 200
revenue is 100(200) = 20000
at 99 members cost per member is 300-2(49) = 202
revenue is 99(202) = 19998 which is less than 20000
at 101 members cost per member is 300-2(51) = 198
revenue is 101(198) = 19998 , which is again less than 20000
My answer is correct.

Similar Questions

1. Math

the total fare for 2 adults and 3 childrren on the Tilt a Whirl ride \$14.00. If a child's fare is 1/2 of an adult's fare, what is the adult fare?

At Mr.Vid's Video Rentals you can join his VId Club for a monthly membership fee pf \$30. Club members pay only \$.85 to rent each movie. If you are not a member of the VID club, the movies rent for \$2.25 each.How many videos would you …
3. math

a cab charges the following fare for ea. trip...first 1/4 mi \$2.95 for every additional 1/4 mi or part \$0.65 (a)what is the fare for a distance of 1 5/8 mi?
4. math math math

HELP ME PLEASE I AM ABOUT TO DIE Should I join the Club?

In a city, the PMV fare is 50 toea. The fare increased by 30%. What is new fare?
6. calculus

A health club offers memberships at the rate of \$300, provided that at least 50 people join. For each member in excess of 50, the membership fee will be reduced by \$2 for all members. Due to space limitations, at most 125 memberships …
7. math

air fare club offers membership at \$300.00, at least 50 people must join.For every member over 50 their fare will be reduced by \$2 for every member. Due to space limits only 125 passengers will be allowed. how many memberships will …
8. Algebra

a City's transit authority serves 178500 communters daily when the fare is \$1.90. Market research has determined that every penny decrease in the fare will result in 1,050 new riders. what fare will maximize revenue?
9. algebra

Matthew would like to join an online book club that costs \$84 per year. If he signs up for an automatic renewal, he will get 5% off his membership. If he signs up in July, he can get an additional 20% off. In addition, for every 2 …
10. Algebra 1

Matthew would like to join an online book club that costs \$84 per year. If he signs up for an automatic renewal, he will get 5% off his membership. If he signs op in July, he will get an additional 20% off. In addition, for every 2 …

More Similar Questions