5. A machine shop makes pipes for the oil and gas industry in lengths of 250...

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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: Machine Lathe Polisher Grinder Minutes per Pipe Short Long 5 7 8 2 10 8 Minutes Available 6300 4000 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. (a) Formulate an algebraic model for the problem. Submit this in Word or pdf. (b) Use LINGO or the Excel Solver to solve this model, including your name and student number on the model. If using LINGO, submit files for the model and the solution for each question. If using the Excel Solver, submit one file for all questions, using tabs for the model and the Answer Report (a total of ten tabs.) (c) State the solution in words. Submit this in Word or pdf. 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: Machine Lathe Polisher Grinder Minutes per Pipe Short Long 5 7 8 2 10 8 Minutes Available 6300 4000 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. (a) Formulate an algebraic model for the problem. Submit this in Word or pdf. (b) Use LINGO or the Excel Solver to solve this model, including your name and student number on the model. If using LINGO, submit files for the model and the solution for each question. If using the Excel Solver, submit one file for all questions, using tabs for the model and the Answer Report (a total of ten tabs.) (c) State the solution in words. Submit this in Word or pdf.