You can now sell 80 cups of lemonade per week at 40¢ per cup, but demand is dropping at a rate of 4 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.]

Question

Mathematics

Jaliyah Cooper

12 August, 12:50

You can now sell 80 cups of lemonade per week at 40¢ per cup, but demand is dropping at a rate of 4 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.]

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Konner Petty · Answer 1

The price will be increased at a rate of 1.05 everyweek to keep my revenue constant.

Step-by-step explanation:

Since demand is dropping at a rate of 4 per week, my next week sales will be (80cups - 4cups = 76cups).

Therefore in order to keep weekly revenue constant I'll have to increase my selling price.

Present revenue = 80cups * 40¢ = 3200¢

For my nextweek revenue which will be (80-4=76 cups) to be at the same 3200¢, I'll use:

Let X be the new price per cul

[ 3200¢ = X * 76]

X = 3200¢/76

X = 42.11¢

Which means I'll need to sell at a rate of 42.11¢ per the next week to keep my revenue the same.

To get the rate [42.11¢ / 40¢ = 1.05]

That means I will be increasing at a rate of 1.05 everyweek to keep my revenue constant.