Search for the unit price of smartness

This is a question about third-level price discrimination. Good weather and bad weather are two divided markets. The optimal price is to realize marginal revenue = marginal cost in the two markets respectively

(1) High temperature marginal benefit = d(QP)/d(Q) = 140-Q

Marginal cost = 20

So Q = 120; price P = 80

Low temperature marginal benefit = d(QP)/d(Q) = 80-Q

Marginal cost = 20

So Q = 60; price P = 50

(2) Because the number of high and low temperature days is equal, the average demand function is the average of the demand functions under the two weather conditions (add the sum and divide by 2)

Average demand function Q=(280-2P)/2+(160-2P)/2=220-2P

Marginal revenue = d(QP)/d(Q)=110-Q

Marginal cost = 20

So Q = 90; price P = 65

(3) High temperature profit = 120* (80-20) = 7200; low temperature profit = 60* ( 50-20)=1800

Average daily profit=7200*0.5+1800*0.5=4500

Profit at constant price=90*(65-20)=4050

The highest cost you are willing to pay=4500-4050=450 points