$6.$ The cartel

Consider a town in which only two residents, Alex and Becky, own wells that produce water safe for drinking. Alex and Becky can pump and sell as much water as they want at no cost$.$ For them, total revenue equals profit. The following table shows the town's demand schedule for water.

$\backslash$table$[[\backslash$table$[[$Price$],[($Dollars per gallon$)]],\backslash$table$[[$Quantity Demanded$],[($Gallons of water$)]],\backslash$table$[[$Total Revenue$],[($Dollars$)]]],[3\mathrm{.}60,0,0],[3\mathrm{.}30,35,115\mathrm{.}50],[3\mathrm{.}00,70,210\mathrm{.}00],[2\mathrm{.}70,105,283\mathrm{.}50],[2\mathrm{.}40,140,336\mathrm{.}00],[2\mathrm{.}10,175,367\mathrm{.}50],[1\mathrm{.}80,210,378\mathrm{.}00],[1\mathrm{.}50,245,367\mathrm{.}50],[1\mathrm{.}20,280,336\mathrm{.}00],[0\mathrm{.}90,315,283\mathrm{.}50],[0\mathrm{.}60,350,210\mathrm{.}00],[0\mathrm{.}30,385,115\mathrm{.}50],[0,420,0]]$

Suppose Alex and Becky form a cartel and behave as a monopolist. The profit$-$maximizing price is $$ per gallon, and the total output is $$ gallons. As part of their cartel agreement, Alex and Becky agree to split production equally. Therefore, Alex's profit is and Becky's profit is $$