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Linear Programming : Solving a production costs problem using the Simplex Method.

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Cauchy Canners produces canned whole tomatoes and tomato sauce. This season, the company has available 3,000,000 kg of tomatoes for these two products. To meet the demands of customers, it must produce at least 80,000 kg of sauce and 800,000 kg of whole tomatoes. The cost per kg is $4 to produce canned whole tomatoes and $3.25 to produce tomato sauce. Labor agreements require that at least 110,000 person-hours be used. Each kilogram can of sauce requires 3 minutes for one worker and each kilogram can of whole tomatoes requires 6 minutes for one worker. How many kilograms of tomatoes should Cauchy use for each product to minimize cost? (for simplicity, assume production of y1 kg of canned whole tomatoes and y2 kg of tomato sauce requires y1 + y2 kg of tomatoes.

A. Select appropriate variables

B. Write objective functions

C. Write constraints of inequalities

D. Solve

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Solution Summary

A production costs problem is solved using the Simplex Method (by hand). The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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  • 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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