Formulate an algebraic model for the problem. Use LINGO or the Excel Solver to solve this model, with your name and student number included in a comment line. Copy-and-paste the model and solution LINGO files. If you solve the models in Excel Solver, you will have to write them in standard form, i.e. all variables on the left-hand side, and a number of the right-hand side. If you use LINGO, you are not bound by this restriction.

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 at a cost of $2 per minute, and can purchase an unlimited amount of extra grinding time at a cost of $3 per minute. For every long pipe made, there must be at least two short pipes made. For every pair of long pipes made, there can be at most seven short pipes made