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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.

##### 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.

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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