its current distribution strategy‚ what will its distribution costs be for the follow quarter? Original shipping plan model MIN 3.2x1+2.2x2+4.2x3+3.9x4+1.2x5+0.3x6+2.1x7+3.1x8+4.4x9+2.7x10+4.7x11+3.4x12+ 2.1x13+2.5x14 DISTRIBUTION CONSTRAINTS 1. x1+x2+x3≤30‚000 2. x4+x5≤20‚000 3. –x1+x6+x7+x8+x9=0 4. –x2-x4+x10+x11+x12=0 5. –x3-x5+x13+x14=0 6. x6=3600 7. x7=4880 8. x8=2130 9. x9=1210 10. x10=6120 11. x11=4830 12. x12=2750 13. x13=8580
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computational procedures will become more apparent in later chapters on network-flow problems and large-scale systems. 4.1 A PREVIEW OF DUALITY We can motivate our discussion of duality in linear programming by considering again the simple example given in Chapter 2 involving the firm producing three types of automobile trailers. Recall that the decision variables are: x1 = number of flat-bed trailers produced per month‚ x2 = number of economy trailers produced per month‚ x3 = number of luxury trailers
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I must admit that I do not fully understand why Lewis chose to include a chapter about animal pain in this book. To me it has no value in his argument about why Man must suffer the problem of pain‚ and seems to not expand the subject at all. While I find this chapter unnecessary‚ I cannot honestly say that upon further readings‚ discussions or thoughts‚ that my opinion will not change‚ but that at the present time this chapter seems wholly out of place in his argument. Lewis closes the book with
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Module A: The Simplex Solution Method PROBLEM SUMMARY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. *13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. *28. *29. *30. 31. 32. 33. 34. Simplex short answer Simplex discussion short answer Simplex short answer Simplex short answer Simplex short answer Simplex short answer 4 tableaus 2 tableaus 3 tableaus 3 tableaus 2 tableaus 5 tableaus 5 tableaus 5 tableaus 6 tableaus 4 tableaus 3 tableaus 3 tableaus 3 tableaus Simplex short answer 3 tableaus 4
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Minimize f ( x1 ‚ x 2 ) = x1 − x 2 + 2 x1 + 2 x1 x 2 + x 2 starting from the point X1 = D L Hooke and Jeeves’ method. Take ∆x1 = ∆x 2 = 0.8 and ε = 0.1. 3 A firm produces three products. These products are processed on three different machines. The time required to manufacture one unit of each of three products and the daily capacity of the three machines are given in the table below: Machine M1 M2 M3 R O Time per unit (minutes) 2 3 2 4 -3 2 5 -- T N W U
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Operational Research Techniques Problem Set: Linear Programming Due: Monday‚ October 20‚ 2014 Please submit to the general office of the IMSE department (Ms Kate Lee HW8-17) on Oct 20 Late submission will be discounted by 20% on a daily basis Please e-mail me msong@hku.hk if you have any questions Problem 1. Work through the simplex method step by step to demonstrate that the following problem is unbounded. (5 marks) max 5x1 + x2 + 3x3 + 4x4 s.t. x1 – 2x2 + 4x3 + 3x4 ≤ 20 –4x1
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minimise the total risk index for the portfolio. b. How much annual income will this investment strategy generate? c. Suppose the client desires to maximise annual return. How should the funds be invested? (ASW: Ch 2‚ Qn 37 – Innis - min) 2. Photo Chemicals produces two types of photographic developing fluids. Both products cost Photo Chemicals $1 per gallon to produce. Based on an analysis of current inventory levels and outstanding orders for the next month‚ Photo Chemicals’
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T-test A t-test is a hypothesis test in which the test statistic follows a Student’s t-distribution under the null hypothesis. There are several different test statistics that fall into the category of a t-test. One-Sample t-test x 0 s n df n 1 t Independent Two-Sample t-test t x1 x2 2 sx1x2 n 1 2 2 sx1 sx2 2 df 2n 2 sx1x2 Unequal Sample Size Two-Sample t-test t x1 x2 1 1 sx1x2 n1 n2 sx1x2 n1 1 sx2 n2
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The Modernist era was a time in which an array of cultural movements established substantial changes in the Western world‚ introducing an industrial society and challenging traditional cultural customs. T.S Eliot has been one of the most daring innovators of twentieth-century poetry‚ and believed that poetry should aim at a representation of the complexities of modern civilization. His poem ‘Preludes’ looks at the decay of the city as a result of ritual‚ futility and the effects of technological
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#3: Case Problem "Julia’s Food Booth" Mat540 Quantitative Methods August 22‚ 2012 Julia’s Food Booth (A) Formulate and solve a L.P. model for this case. Variables: Pizza - X1 $1.33 $1.50 14 inches Hot Dogs - X2 $0.45 $1.50 16 square inches Barbecue - X3 $0.90 $2.25 25 square inches Maximize Z= $0.75x1‚ 1.05x2‚ 1.35x3 Subject to: $0.75x1 + $0.45x2 + $0.90x3 ≤ $1‚500 24x1 + 16x2 + 25x3 ≤ 55‚296 in2 of oven space x1 ≥ x2 + x3 (changed to –x1 + x2 + x3 ≤ 0 for constraint)
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