‘The Pastry’ is a leading chain of bakery shops in Mumbai. They accept bulk orders of their award winning cakes for parties. Their churning machine produces 100 litres of batter every morning. The cost price of the batter is Rs. 0.25 per cubic centimetre. This batter is then poured into molds up to their brims and baked to make the cakes. The batter left over at the end of the day gets spoilt and hence is discarded. The chefs at ‘The Pastry’ bend metallic sheets along the width into the shape of a regular polygon to form the molds. The molds are then placed on a baking tray after which the batter is poured in them. Each metallic sheet has unit width (in cm) and 60 cm length. On a certain day, ‘The Pastry’ received only one order. The client wants them to provide cakes of exactly two shapes and to charge Rs 70/- per cake after the delivery. ‘The Pastry’ wants to maximize its profits and minimize the wastage from this order. Can you help them in doing so? What is the maximum profit that they can make and how much batter gets wasted?
Since the people at ‘The Pastry’ do not like calculations, they stop their calculations after obtaining the first post-decimal digit. Since the number of cakes is always a natural number, the calculations stop immediately after the unit’s digit is obtained.