A supermarket bakery must decide how many birthday cakes to prepare for the upcoming weekend. Cakes cost INR $500$ each, and they sell for INR $900$ each. Unsold cakes are reduced to half$-$price on Monday; typically, two$-$thirds are sold. Any that remain are donated to an orphanage. The demand data over the past four months is indicated in the following table. How many cakes should be prepared to maximize expected profit?A supermarket bakery must decide how many birthday cakes to prepare for the upcoming weekend.

Cakes cost INR $500$ each, and they sell for INR $900$ each. Unsold cakes are reduced to half$-$price

on Monday; typically, two$-$thirds are sold. Any that remain are donated to an orphanage. The

demand data over the past four months is indicated in the following table. How many cakes should

be prepared to maximize expected profit?