# Operations Research: Maximizing Profit

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A factory can assemble printers and scanners. The 50 factory workers operate three four hour shifts which keep the factory running for a total of 12 hours a day, 6 days a week. Before the printers and scanners can be assembled, the component parts must be purchased and the maximum value of the stock that can be held for a days assembly work is £1020.

In the factory, a printer takes 1 hour 20 minutes to assemble using £20 worth of components whereas a scanner takes 30 minutes to assemble using £60 worth of components. The profit made on a printer is £10 and on a scanner is £15.

a) Summarize the above information in a table

b) Assuming that the factory can sell all the printers and scanners that it assembles, formulate the above information into a Linear Programming problem.

c) Determine the number of printers and the number of scanners that should be made in a day to maximize profit (not using Simplex Method).

d) The market for printers is becoming increasingly competitive which is driving down profits. How long can the profit on a printer go before the optimal solution moves to another corner point of the feasible region? When the profit on a printer does drop below this level, what should the factory produce to maximize its profits? What is the maximum profit in this case?

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##### Solution Summary

Linear programming is used to define constraints and calculate a maximum profit.

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