Problem
It's about 1500. The pope needs the roof of a big cathedral chapel painted. It's 400 square meters. He needs to hire a master painter, who does no actual work on the ceiling, at 8 solidi per day, plus a number of journeyman painters, who can paint 10 square meters each in a day and make 2 solidi per day. He also needs to provide frocks and brushes for each painter hired, and that comes to an extra cost of 10 solidi per painter hired. How many painters should the pope hire to minimize the cost of painting the roof, and most importantly, how much will it cost? Redo if :
i. The master painter has to be paid 20 solidi per day instead of 8
ii. The journeymen have to be paid 4 solidi per day instead of 2
iii. The journeymen can paint 20 m2 per day instead of 10
iv. It's 1550 instead of 1500