3. In Thirsty City, daily demand for water is given by the function D = 100 − p/2 where demand is measured in millions of gallons per day (mgd) and p is the price of a million gallons of water. If the regular water supply runs out, bottled water can be imported into Thirsty City endlessly at a cost of $80 per million gallons.

Thirsty City’s reservoir has a capacity of 350 million gallons. Every Sunday it rains the same way: enough rain falls that 490 million gallons could be deposited in the reservoir if it didn’t spill over. The Sunday rain storms are absolutely certain. The rate of interest is zero, and no water ever evaporates.

What’s the optimal price of water on each day of the week in Thirsty City? (Decide whether the optimal price is different on different days.) How much water is consumed every day?