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    Mathematical Model on Standard and Deluxe Bags

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    Problem # 1

    The following is the current mathematical model for the production of Standard and Deluxe Bags by Par Manufacturing.

    Max 10s + 9d
    s.t.

    7/10s +1d is < or equal to 630
    1/2s + 5/6 d < or equal to 600
    1s + 2/3 d < or equal to 708
    1/10s + 1/4d < or equal to 135

    S, D, > or equal to 0

    Optimal Solution = (540,252)
    Optimal Value = 10(540) + 9(252)
    = 5400 + 2268
    = 7668

    Now, suppose that management encounters the following situations.

    1) The accounting dept revises its estimate of the profit contribution for the deluxe bag to $18 per bag
    2) The profit contribution per standard bag can be increased to $20 per bag(Assume the profit contribution for the deluxe bag is the original $9 value)
    3) The sewing operation capacity has increased to 750 Hours (Assume that 10s + 9d is the appropriate objective function)

    If each of these situations is encountered separately, what is the optimal solution and the total profit contribution.

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    https://brainmass.com/statistics/descriptive-statistics/mathematical-model-standard-deluxe-bags-25335

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    Solution Summary

    The following is the current mathematical model for the production of Standard and Deluxe Bags by Par Manufacturing.

    Max 10s + 9d
    s.t.

    7/10s +1d is < or equal to 630
    1/2s + 5/6 d < or equal to 600
    1s + 2/3 d < or equal to 708
    1/10s + 1/4d < or equal to 135

    S, D, > or equal to 0

    Optimal Solution = (540,252)
    Optimal Value = 10(540) + 9(252)
    = 5400 + 2268
    = 7668

    Now, suppose that management encounters the following situations.

    1) The accounting dept revises its estimate of the profit contribution for the deluxe bag to $18 per bag
    2) The profit contribution per standard bag can be increased to $20 per bag(Assume the profit contribution for the deluxe bag is the original $9 value)
    3) The sewing operation capacity has increased to 750 Hours (Assume that 10s + 9d is the appropriate objective function)

    If each of these situations is encountered separately, what is the optimal solution and the total profit contribution.

    $2.49

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