# LP Problem on Maximizing Profit

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Consider the following LP problem:

maximize profit= 5x+6y

subject to: 2x + y _< 120

2x + 3y _< 240

x,y _< 0

The profit for product x is $5 and for product y is $6. To maximize profit in this linear program, the solution was to manufacture 30 product x and 60 product y. What is the total profit from product x for this production mix?

A. 150

B. 510

C. 240

D. 1.75

E. none of the above

Note: _< means less than or equal to! I didn't know how to type it correctly

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##### Solution Summary

Uses the simplex method and a couple tableaus to solve a maximization LP problem.

##### Solution Preview

Tableau #1

x y s1 s2 p

2 1 1 0 0 120

2 3 0 1 0 240

-5 -6 ...

###### 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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