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# Linear Programming for profit optimization

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The Exeter Company produces two basic types of dog toys. Two resources are crucial to the output of the toys: assembling hours and packaging hours. Further, only a limited quantity of type 1 toy can be sold. The linear programming model given below was formulated to represent next weekÃ¢Ã¢?Â¬Ã¢?Â¢s situation.
Let, X1 = Amount of type A dog toy to be produced next week
X2 = Amount of type B dog toy to be produced next week
Maximize total contribution Z = 35 X1 + 40 X2
Subject to
Extrusion hours: 4 X1 + 6 X2 Ã¢Ã¢?Â°Â¤ 48
Packaging hours: 2 X1 + 2 X2 Ã¢Ã¢?Â°Â¤ 18
Sales Potential: X1 < 6
Non-negativity: X1 Ã¢Ã¢?Â°Â¥ 0, X2 Ã¢Ã¢?Â°Â¥ 0
Use Excel Solver OR graphical method to find the optimal solution of the problem. If you use Excel Solver, please paste your output here.
Note 1: Place X1 along the horizontal axis and X2 along the vertical axi.
Note 2: Clearly mark the feasible region on the graph.
Note 3: Find the points of intersection points algebraically.
Note 4: Clearly show all steps to find the optimal solution by the graphical method.