(a) Formulate a model for this problem, taking care to define 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 profit of $150 each, while each long pipe gives a profit 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 Short Long 7 2 8 Machine Lathe 5 Polisher 8 Grinder 10 Minutes Available 4900 4500 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 five short pipes made.