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Intro Mgmt Sci

Intro Mgmt Sci. 472.21 3 Fall 2011 Bruce Duggan. This week. work together on ch 2 & 3 problems particularly “model formulation” (math) dealing with ratios goal develop a standard “system” to attack each problem quiz Fri fair game all ch 2 problems probs 1 – 33 will only ask

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Intro Mgmt Sci

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  1. Intro Mgmt Sci 472.21 3 Fall 2011 Bruce Duggan

  2. This week • work together on ch 2 & 3 problems • particularly • “model formulation” (math) • dealing with ratios • goal • develop a standard “system” to attack each problem • quiz Fri • fair game • all ch 2 problems • probs 1 – 33 • will only ask • write the linear program (the math)

  3. St. A Craft League • Model formulation: • l.p. Max Z = $40x1 + $50x2 s.t. 1x1 + 2x2 40 4x1 + 3x2 120 x1, x2 0

  4. Problems • review ch 2 problems • in group • 2 • 38 • yourself • 1 • 16

  5. Remember St. Adolpe Craft League: We need a “standard” approach to produce a formula like this for each problem. Problems Max Z = $40x1 + $50x2 s.t. 1x1 + 2x2 40 4x1 + 3x2 120 x1, x2 0

  6. Problems min or max? decision variables objective function constraints a “standard” approach

  7. Problems min or max? decision variables outputs products some sort of result What are we trying to produce? how many of product 1? how many of product 2? how many of product…? a “standard” approach x1 x2 …xn

  8. Problems min or max? decision variables objective function a “standard” approach Max Z = z1x1 + z2x2 +…znxn Min Z = z1x1 + z2x2 +…znxn

  9. Problems min or max? decision variables objective function constraints inputs resources (max) requirements (min) a “standard” approach • non-negativity constraints • integer constraints • ratio requirements

  10. Problems min or max? decision variables objective function constraints non-negative: integer constraint: a “standard” approach • max: a1x1 + a2x2 aavailable b1x1 + b2x2 bavailable … n1x1 + n2x2 navailable • min: xi0 a1x1 + a2x2 arequired b1x1 + b2x2 brequired … x?=0 or 1 n1x1 + n2x2 nrequired

  11. Problems • 2: “A Company” • min or max? • max

  12. Problems • 2: “A Company” • min or max? • decision variables • how many of product 1? • how many of product 2? x1 x2

  13. Problems • 2: “A Company” • min or max? • decision variables • objective function Max Z = z1x1 + z2x2 Max Z = $6.00x1 + $4.00x2

  14. Problems • 2: “A Company” • min or max? • decision variables • objective function • constraints • time available on line 1 • time available on line 2 a 100 hours b 42 hours 10x1 + 10x2100 hours a1x1 + a2x2 aavailable 7x1 + 3x242 hours b1x1 + b2x2 bavailable

  15. Problems • 2: “A Company” Max Z = z1x1 + z2x2 Max Z = $6.00x1 + $4.00x2 s.t. a1x1 + a2x2 aavailable s.t. 10x1 + 10x2100 hours b1x1 + b2x2 bavailable 7x1 + 3x242 hours xi0 x1, x20

  16. Problems • 38: “A Manufacturing Firm” • min or max? • decision variables • objective function • constraints

  17. Problems • 38: “A Manufacturing Firm” • min or max? • max

  18. Problems • 38: “A Manufacturing Firm” • min or max? • decision variables • how many of product 1? • how many of product 2? x1 x2

  19. Problems • 38: “A Manufacturing Firm” • min or max? • decision variables • objective function Max Z = z1x1 + z2x2 Max Z = $30.00x1 + $70.00x2

  20. Problems • 38: “A Manufacturing Firm” • min or max? • decision variables • objective function • constraints • assembly hours • finishing hours • warehouse space a 80 hours b 112 hours c space for 10 units

  21. Problems • 38: “A Manufacturing Firm” Max Z = z1x1 + z2x2 Max Z = $30.00x1 + $70.00x2 s.t. a1x1 + a2x2 aavailable s.t. 4x1 + 10x280 hours b1x1 + b2x2 bavailable 14x1 + 8x2112 hours c1x1 + c2x2 cavailable x1 + x210 spaces xi0 x1, x20

  22. Problems • 1: Marie baking for the PTA • min or max? • max

  23. Problems • 1: Marie baking for the PTA • min or max? • decision variables • how many cakes? • how many loaves of bread? x1 x2

  24. Problems • 1: Marie baking for the PTA • min or max? • decision variables • objective function Max Z = z1x1 + z2x2 Max Z = $10.00x1 + $6.00x2

  25. Problems • 1: Marie baking for the PTA • min or max? • decision variables • objective function • constraints • cups of flour • cooking time a 20 cups b 180 minutes

  26. Problems • 1: Marie baking for the PTA Max Z = z1x1 + z2x2 Max Z = $10.00x1 + $6.00x2 s.t. a1x1 + a2x2 aavailable s.t. 3x1 + 8x220 cups b1x1 + b2x2 bavailable 45x1 + 30x2180 min. x1, x20 and integer xi0 and integer

  27. Problems • 16: “A Clothier” • min or max? • max

  28. Problems • 16: “A Clothier” • min or max? • decision variables • how many coats? • how many pairs of slacks? x1 x2

  29. Problems • 16: “A Clothier” • min or max? • decision variables • objective function Max Z = z1x1 + z2x2 Max Z = $50.00x1 + $40.00x2

  30. Problems • 16: “A Clothier” • min or max? • decision variables • objective function • constraints • square yards of wool • hours of labour a 150 square yards b 200 hours

  31. Problems • 16: “A Clothier” Max Z = z1x1 + z2x2 Max Z = $50.00x1 + $40.00x2 s.t. a1x1 + a2x2 aavailable s.t. 3x1 + 5x2150 sq. yards b1x1 + b2x2 bavailable 10x1 + 4x2200 hours x1, x20 and integer xi0 and integer

  32. Problems min or max? decision variables objective function constraints inputs resources (max) requirements (min) a “standard” approach • non-negativity constraints • integer constraints • ratio requirements

  33. Problems ratio requirements “no more than…” “at least…” “equal to…” must be referring to the decision variables the x’s the outputs a “standard” approach

  34. Problems ratio requirements a “standard” approach write out a sentence for each requirement break apart if possible rewrite sentences using symbols: x  = write ratios rearrange so that: unequal signs pointing same way as other constraints all on single line (no fractions) x’s on left side of equation x’s in order 0 on right side a “standard” approach

  35. The Possibility Restaurant ratios at least 3 fish for every 2 beef at least 10% will order beef

  36. The Possibility Restaurant ratios at least 3 fish for every 2 beef

  37. The Possibility Restaurant ratios at least 10% beef

  38. The Possibility Restaurant

  39. Let’s solve some problems • Xecko Tool • ch 3 pg 95 9th ed • Southern Sporting Goods • ch 3 prob 5-7 pg 96-97 • Food Max • ch 3 prob 40-41 pg 104 no graphs no “sensitivity analysis” yet not “standard form” yet formulas Excel

  40. Xecko Tool • bidding on a job • manufacturing processes

  41. Southern Sporting Goods • makes basketballs & footballs • manufacturing processes

  42. Food Max • how much milk to stock

  43. Your turn • Irwin Textile Mills • ch 3 prob 11-13 pg 98 • 12a, 12b, 12c • United Aluminium Company • ch 3 prob 14-16 pg 98-99 • 15a, 15b, 15c, 16c l.p. Excel no graph

  44. Working On • Possibility Restaurant • pg 70 • don’t do “what if”s in last paragraph • Irwin Textile Mills • ch 3 prob 11-13 pg 98 • 12a, 12b, 12c • United Aluminium Company • ch 3 prob 14-16 pg 98-99 • 15a, 15b, 15c, 16c l.p. Excel no graph

  45. The Possibility Restaurant But what about ratios?

  46. Irwin Textile Mills

  47. United Aluminium

  48. To Do • Julia’s Food Booth • ch 3 case 3 pg 98-99 • A, B, C, D • Exeter Mines • ch 3 prob 48-49 pg 105 • 12a, 12b, 12c

  49. Next Week • Sensitivity • Chapter 4 • more applications

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