(a) Formulate a model for this problem, taking care to dene each of the variables used. (b) Solve the model using Excel. (c) State the recommendation. . A machine shop makes pipes for the oil and gas industry in lengths of 240 cm and 400 cm. The shorter pipes give a prot of $150 each, while each long pipe gives a prot of $270. They can sell at most 900 of the 240 cm pipes and at most 800 of the longer ones. Each pipe spends time on three machines as follows: Minutes per Pipe Minutes Machine Short Long Available Lathe 5 7 4900 Polisher 8 2 4500 Grinder 10 8 7200 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 ve short pipes made