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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 weekââ?¬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 ââ?°¤ 48
    Packaging hours: 2 X1 + 2 X2 ââ?°¤ 18
    Sales Potential: X1 < 6
    Non-negativity: X1 ââ?°¥ 0, X2 ââ?°¥ 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.

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    Solution Summary

    LP is formulated and a graphical method is used to find the feasible region and optimized solution.