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Linear Programming:Maximization of Profit

The Artful Dodger Sports Shop is sponsoring a weekly boomerang throwing contest as part of its spring promotions. Anyone may enter, but the boomerangs uses must be purchased at the The Artful Dodger. Because a smooth finish on the boomerang is essential for accurate flight, most entrants to the contest are expected to buy a new boomerang every few weeks. Therefor, The Artful Dodger expects to sell all that it can produce.

Two models can be produced: the regular model (with a profit of $2 each), and the "Super Bender" (with a profit of $5 each). Production facilities are limited. A regular boomerang an hour of carving and 2 hours of finishing. A "Super Bender" takes 3 hours to carve and 2 hours to finish. Skilled artisans employed by the Artful Dodger have indicated that they will spend no more than 75 hours carving and 100 hours finishing boomerangs per week.

a) Formulate a linear programming model to determine the number of each type of boomerang that should be produced each week, seeking maximum profit.

b) Solve this model with the graphical method.

*With this study problem, what I am seeking is a step-by-step process that I can understand and utilize.

Solution Summary

The solution provides step by step method for the calculation of optimal solution for a maximization problem using graphical method. Graph of the feasible region is also included.