1. You can now sell 50 cups of lemonade per week at 40¢ per cup, but demand is decreasing at the rate of 5 cups per week each week. Suppose that increasing price doesn't affect demand, how fast you have to raise the price if you want to keep the weekly revenue constant?
2. You now can sell 60 cars per month at $30,000 per car, and demand is increasing at the rate of 3 cars per month each month. Determine fastest you could drop the price before the monthly revenue begins to drop?
3. The demand equation for rubies at Royal Ruby Retailers is
q+1/2p=70
where q is number of rubies RRR can sell per week at p dollars per ruby. RRR finds that demand for its rubies is presently 15 rubies per week and is decreasing at the rate of one ruby per week. How fast is price varying?