MATH2730 – Operations Research I Project Due: 9am Thursday 9th May 2013 An engineering products manufacturer has a factory which makes several products. Each product may require time on one or more of a number of different machines, for example, a grinder, horizontal drill, or grinder. An example with seven products, and five types of machines is given in Table 11. Assume the machines required to make a product can be used in any order. During any particular planning period company has one or more machines of each type available for work the factory. For example, it may have four grinders, two vertical drills, three horizontal drills, one borer and one planer. The company plans monthly production over a planning period of some number of months, for example, 6 months. In each month, the company must decide how many units to manufacture, of each product. Production is constrained by the number of hours the factory is working each month, for example, if the factory works a 6-day week, with two shifts of 8 hours each, and there are four weeks per month, then that corresponds to the factory (and all machines in it) being available to work 6284 = 384 hours per month. Each product brings in a certain amount of revenue, per unit sold, and costs a certain amount per unit for manufacturing. Furthermore, market constraints in each month set upper limits on how much can be sold in that month. Sample revenue, costs and market limits are given in Table 2. Product can be manufactured early, and held in a warehouse for sale in a later month. The product units have been scaled so that the total number of units of all products to be stored can be added to deduce the amount of space used in the warehouse: there is an overall warehouse capacity in terms of number of (any and all) products. For example, it may be that the warehouse can hold no more than 700 units of products at any one time. Storage cost per unit of each product held per month has been estimated, for example, it may be…