5. A machine shop makes pipes for the oil and gas industry in lengths of 250 cm and 400 cm. The shorter pipes give a profit of $140 each, while each long pipe gives a profit of $270. They can sell at most 900 of the 250 cm pipes and at most 300 of the longer ones. Each pipe spends time on three machines as follows: Minutes per Pipe Minutes Machine Short Long Available Lathe 5 7 6300 Polisher 8 2 4000 Grinder 10 8 8100 In addition to the minutes available given in the above table, they can purchase up to 500 minutes (all, none, or any fraction of this amount) of additional polishing time