The manager of a 240-room ski resort has found that, on average, 150 rooms are booked when the price is $175 per night and 160 rooms are booked when the price is $160 per night. What price should the manager set for the rooms to maximize revenue?
2007-01-08 16:14:22 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
You have to know what sort of relationship there is. I assume, since nothing was given, that the relationship is linear?
In that case, the equation becomes:
b = 800/3 - 2c/3
Now, revenue is found by (rooms booked)*(cost per room), or
R = bc
R = 800c/3 - 2c²/3
Now, we want to maximize this. Obviously, we can multiply by 3 and not change the point of maximum:
f = 800c - 2c²
Now take the derivative and find the zero:
f' = 800 - 4c
0 = 800 - 4c
4c = 800
c = 200
The price which maximizes revenue is $200 per night, and will result in 133 rooms being booked. The maximum revenue is $26,600.
2007-01-08 16:34:54 · answer #1 · answered by computerguy103 6 · 0⤊ 0⤋
150=$175
160=$160
+10 rooms= -$5
max 240 rooms
240-150=90
90/10=9
9*5=45
$175-$45=$130
2007-01-09 00:26:31 · answer #2 · answered by kt 2 · 0⤊ 1⤋
if this is the only info you give the answer is the max of (150*175 and 160*160)
2007-01-09 01:03:12 · answer #3 · answered by gjmb1960 7 · 0⤊ 0⤋
about $40... It's just a guess that if the price goes down about 8.6% and ten more rooms get filled, then just keep subtracting 8.6% until you get to 240 rooms and about $40 is the price that you have.
2007-01-09 00:23:24 · answer #4 · answered by Tim 2 · 0⤊ 1⤋