You can now sell 50 cups of lemonade per week at 50¢ per cup?
You can now sell 50 cups of lemonade per week at 50¢ per cup, but demand is dropping at a rate of 3 cups per week each week. Assuming that raising the price does not affect demand, how fast do you have to raise your price if you want to keep your weekly revenue constant? HINT [Revenue = Price × Quantity.]
_____¢ per week
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Revenue = 50 cups * 50c = $25
It's not linear.
Required price in week n in cents
(where n = 0 in the initial 50 cups/week week)
=
2500 / (50 - 3*n)
Required increase = 2500 / (50 - 3(n-1)) - (2500 / (50 - 3n))
# sold ... price . . . . increase from previous week
50 ... 0.50 ...
47 ... 0.53 ... 0.03
44 ... 0.57 ... 0.04
41 ... 0.61 ... 0.04
38 ... 0.66 ... 0.05
35 ... 0.71 ... 0.06
32 ... 0.78 ... 0.07
29 ... 0.86 ... 0.08
26 ... 0.96 ... 0.10
23 ... 1.09 ... 0.13
20 ... 1.25 ... 0.16
17 ... 1.47 ... 0.22
14 ... 1.79 ... 0.32
11 ... 2.27 ... 0.49
8 ... 3.13 ... 0.85
5 ... 5.00 ... 1.88
2 ... 12.50 ... 7.50
Those $5.00 and $12.50 lemonades might prove a tough sell.
50 Cups