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# Linear Programming

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Baseball Inc produces Regular gloves and Catcher?s mitt. The linear programming problem is listed below:

Max 5R + 8C
s.t.
R + 3C < or equal to 1800 Cutting dept
3R + 2C < or equal to 1800 Finishing dept
R + 2C < or equal to 800 Packaging dept

R, C, > or equal to 0

The computer solution obtained using the Management Scientist is attached (see Figure A). Use the computer solution to answer the following questions:

1) what is the optimal solution
2) What is the value of the total profit contribution
3) Which constraints are binding
4) What are the dual prices for the resources. Interpret each.
5) If overtime can be scheduled in one of the departments, where would you recommend doing so.
6) What does the 100% Rule in relation to the Allowable Increases and Allowable decreases mean in this example. Explain the concept with an example.

##### Solution Summary

The optimal solution is found. The expert determines what the value of the total profit contribution is. The binding constraints are analyzed.

Solution provided by:
###### 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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