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Operations Research: Maximizing Profit

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?

Solution Summary

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