# Mathematical Model on Standard and Deluxe Bags

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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#### 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.