Leatherco is contracted to manufacture batches of pants, vests, and jackets. Each product requires a special...

  

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Leatherco is contracted to manufacture batches of pants, vests, and jackets. Each product requires a special setup of the machines needed in the manufacturing processes. The following table provides the pertinent data regarding the use of raw material (leather) and labor time together with cost and revenue estimates. Current supply of leather is estimated at 3800 ft², and available labor time is limited to 2850 hours. Leather material per unit (ft²) Labor time per unit (hr) Production cost per unit (S) Equipment setup cost per batch ($) Price per unit ($) Minimum number of units needed Theater location Movies offerings In-town 1,3 City A 1,6,8 City B 2,5,7 City C Pants City D City E City F 5.5 4.5 1,8,9 2,4,7 1,3,5, 10 4,5,6,9 30 110 60 100 Vests Determine the optimum number of units that Leatherco must manufacture of each product. 3.5 3.5 . Bill has just completed his exams for the academic year and wants to celebrate by seeing every movie showing in theaters in his town and in six other neighboring cities. If he travels to another town, he will stay there until he has seen all the movies he wants. The following table provides the information about the movie offerings and the round-trip distance to the neighboring town. 0 25 30 28 40 20 90 40 150 Round-trip miles 35 32 Jackets 7.5 5.5 80 140 120 200 Cost per show ($) 7.95 5.50 5.00 7.00 4.95 5.25 6.75 The cost of driving is 75 cents per mile. Bill wishes to determine the towns he needs to visit to see all the movies while minimizing his total cost. The Record-a-Song Company has contracted with a rising star to record eight songs. The sizes in MB of the different songs are 8, 10, 8, 7, 9, 6, 7, and 12, respectively. Record-a- Song uses two CDs for the recording. Each CD has a capacity of 40 MB. The company would like to distribute the songs between the two CDs such that the used space on each CDs is about the same. Formulate the problem as an ILP, and find the optimum solution. Develop the B&B tree for each of the following problems. For convenience, always select x₁ as the branching variable at node 0. *(a) Maximize z = 3x₁ + 2x₂ subject to (b) Maximize z = subject to 2x1 + 5x₂ = 18 4x₁ + 2x₂ 18 X1, X₂0 and integer 2x1 + 3x₂ (e) Maximize z = 2x₁ + 2x₂ subject to (d) Minimize z = 5x₁ + 4x₂ subject to (e) Maximize z = 5x₁ + 7x₂ subject to 7x₁ + 5x₂ = 36 4x₁ + 9x₂ ≤ 35 X1, X20 and integer 2x1 + 5x₂ = 27 6x₁ + 5x₂ = 16 X1, X₂0 and integer 3x₁ + 2x₂ = 5 2x₁ + 3x₂ = 7 X₁, X₂0 and integer 2x₁ + x2₂ 13 5x₁ + 9x₂ = 41 x₁, x₂0 and integer Leatherco is contracted to manufacture batches of pants, vests, and jackets. Each product requires a special setup of the machines needed in the manufacturing processes. The following table provides the pertinent data regarding the use of raw material (leather) and labor time together with cost and revenue estimates. Current supply of leather is estimated at 3800 ft², and available labor time is limited to 2850 hours. Leather material per unit (ft²) Labor time per unit (hr) Production cost per unit (S) Equipment setup cost per batch ($) Price per unit ($) Minimum number of units needed Theater location Movies offerings In-town 1,3 City A 1,6,8 City B 2,5,7 City C Pants City D City E City F 5.5 4.5 1,8,9 2,4,7 1,3,5, 10 4,5,6,9 30 110 60 100 Vests Determine the optimum number of units that Leatherco must manufacture of each product. 3.5 3.5 . Bill has just completed his exams for the academic year and wants to celebrate by seeing every movie showing in theaters in his town and in six other neighboring cities. If he travels to another town, he will stay there until he has seen all the movies he wants. The following table provides the information about the movie offerings and the round-trip distance to the neighboring town. 0 25 30 28 40 20 90 40 150 Round-trip miles 35 32 Jackets 7.5 5.5 80 140 120 200 Cost per show ($) 7.95 5.50 5.00 7.00 4.95 5.25 6.75 The cost of driving is 75 cents per mile. Bill wishes to determine the towns he needs to visit to see all the movies while minimizing his total cost. The Record-a-Song Company has contracted with a rising star to record eight songs. The sizes in MB of the different songs are 8, 10, 8, 7, 9, 6, 7, and 12, respectively. Record-a- Song uses two CDs for the recording. Each CD has a capacity of 40 MB. The company would like to distribute the songs between the two CDs such that the used space on each CDs is about the same. Formulate the problem as an ILP, and find the optimum solution. Develop the B&B tree for each of the following problems. For convenience, always select x₁ as the branching variable at node 0. *(a) Maximize z = 3x₁ + 2x₂ subject to (b) Maximize z = subject to 2x1 + 5x₂ = 18 4x₁ + 2x₂ 18 X1, X₂0 and integer 2x1 + 3x₂ (e) Maximize z = 2x₁ + 2x₂ subject to (d) Minimize z = 5x₁ + 4x₂ subject to (e) Maximize z = 5x₁ + 7x₂ subject to 7x₁ + 5x₂ = 36 4x₁ + 9x₂ ≤ 35 X1, X20 and integer 2x1 + 5x₂ = 27 6x₁ + 5x₂ = 16 X1, X₂0 and integer 3x₁ + 2x₂ = 5 2x₁ + 3x₂ = 7 X₁, X₂0 and integer 2x₁ + x2₂ 13 5x₁ + 9x₂ = 41 x₁, x₂0 and integer

Answer rating: 100% (QA)

Okay here are the full steps solving each problem a BB tree for problem a Node 0 x1 0 LHS 30 2x2 18 ... View the full answer