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(a) Develop the linear programming formulation of this problem. (Let XA₁ be the number of units of product A produced by machine 1, x,, be the number of units of product i produced by machine j, etc.) +1.2%3B +1.2x30 Min 1x14 +1.1x10 +1.2x24 +1.4x2B + 1x2C+0.9x34 +1.3x1B Check which variable(s) should be in your answer. s.t. Machine 1 Capacity Machine 2 Capacity Machine 3 Capacity Product A Orders Product B Orders Product C Orders 1x₁4 +1x1B+1x1c≤1800 X Check which variable(s) should be in your answer. 1x24+1x2B + 1x₂0 ≤1700 X Check which variable(s) should be in your answer. 1x24 + 1x2B + 1x2c≤ 800 X Check which variable(s) should be in your answer. *14+*24 +34 = 2200 X Check which variable(s) should be in your answer. *1B+X₂B+X3B = 300 X Check which variable(s) should be in your answer. *1c+x₂c+x3c=1400 X Check which variable(s) should be in your answer. xi, 2 0 for all i, j. (b) Solve the transportation model for the minimum cost production schedule for the products and machines. Show the production schedule. (XA1 XA2 XA3 XB1 X62 X83 XC1 C2 XC3) = 1400,300,0,0,0,1400,800,0,0 Determine the cost (in dollars) of the production schedule. Total = $ 3910 x X X )

(a) Develop the linear programming formulation of this problem. (Let XA₁ be the number of units of product A produced by machine 1, x,, be the number of units of product i produced by machine j, etc.) +1.2%3B +1.2x30 Min 1x14 +1.1x10 +1.2x24 +1.4x2B + 1x2C+0.9x34 +1.3x1B Check which variable(s) should be in your answer. s.t. Machine 1 Capacity Machine 2 Capacity Machine 3 Capacity Product A Orders Product B Orders Product C Orders 1x₁4 +1x1B+1x1c≤1800 X Check which variable(s) should be in your answer. 1x24+1x2B + 1x₂0 ≤1700 X Check which variable(s) should be in your answer. 1x24 + 1x2B + 1x2c≤ 800 X Check which variable(s) should be in your answer. *14+*24 +34 = 2200 X Check which variable(s) should be in your answer. *1B+X₂B+X3B = 300 X Check which variable(s) should be in your answer. *1c+x₂c+x3c=1400 X Check which variable(s) should be in your answer. xi, 2 0 for all i, j. (b) Solve the transportation model for the minimum cost production schedule for the products and machines. Show the production schedule. (XA1 XA2 XA3 XB1 X62 X83 XC1 C2 XC3) = 1400,300,0,0,0,1400,800,0,0 Determine the cost (in dollars) of the production schedule. Total = $ 3910 x X X )

Contemporary Marketing
Contemporary Marketing
18th Edition
ISBN:9780357033777
Author:Louis E. Boone, David L. Kurtz
Publisher:Louis E. Boone, David L. Kurtz
Chapter15: Distribution Channels And Supply Chain Management
Section15.4: Components Of The Supply Chain
Problem 1LO
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The Ace Manufacturing Company has orders for three similar products. Orders (units) Product A B с 1 2 Machine 3 A Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A B B IC c с Product 1 2 2,200 3 300 1,400 Capacity (units) 1,800 1,700 800 1 Machine 2 3 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20
Transcribed Image Text:The Ace Manufacturing Company has orders for three similar products. Orders (units) Product A B с 1 2 Machine 3 A Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A B B IC c с Product 1 2 2,200 3 300 1,400 Capacity (units) 1,800 1,700 800 1 Machine 2 3 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20
(a) Develop the linear programming formulation of this problem. (Let XA1 be the number of units of product A produced by machine 1, x; be the number of units of product i produced by machine j, etc.) X₁ Min 1x14 +1.3x1B + 1.1x10+1.2x24 +1.4x2B + 1x2c +0.9x34 +1.2x3B+1.2x30 Check which variable(s) should be in your answer. s.t. Machine 1 Capacity Machine 2 Capacity Machine 3 Capacity Product A Orders Product B Orders Product C Orders 1x14+ 1x1B + 1x1C ≤ 1800 X Check which variable(s) should be in your answer. 1x24 + 1x2B + 1x2C≤1700 X Check which variable(s) should be in your answer. 1x24+ 1x2B + 1x₂C≤800 X Check which variable(s) should be in your answer. *14+*24+x34 = 2200 X Check which variable(s) should be in your answer. |X1B+X2B+X3B = 300 X Check which variable(s) should be in your answer. |*1c+x₂c + x3c=1400| X Check which variable(s) should be in your answer. X X¡i¡ 2 0 for all i, j. (b) Solve the transportation model for the minimum cost production schedule for the products and machines. Show the production schedule. (XA1¹ XA2¹ ×A3¹ ×81¹ ×82¹ ×83¹ ×C1₁¹ *c2′ Xc3) = ( 1400,300,0,0,0,1400,800,0,0 |x) Determine the cost (in dollars) of the production schedule. Total = $ 3910 X
Transcribed Image Text:(a) Develop the linear programming formulation of this problem. (Let XA1 be the number of units of product A produced by machine 1, x; be the number of units of product i produced by machine j, etc.) X₁ Min 1x14 +1.3x1B + 1.1x10+1.2x24 +1.4x2B + 1x2c +0.9x34 +1.2x3B+1.2x30 Check which variable(s) should be in your answer. s.t. Machine 1 Capacity Machine 2 Capacity Machine 3 Capacity Product A Orders Product B Orders Product C Orders 1x14+ 1x1B + 1x1C ≤ 1800 X Check which variable(s) should be in your answer. 1x24 + 1x2B + 1x2C≤1700 X Check which variable(s) should be in your answer. 1x24+ 1x2B + 1x₂C≤800 X Check which variable(s) should be in your answer. *14+*24+x34 = 2200 X Check which variable(s) should be in your answer. |X1B+X2B+X3B = 300 X Check which variable(s) should be in your answer. |*1c+x₂c + x3c=1400| X Check which variable(s) should be in your answer. X X¡i¡ 2 0 for all i, j. (b) Solve the transportation model for the minimum cost production schedule for the products and machines. Show the production schedule. (XA1¹ XA2¹ ×A3¹ ×81¹ ×82¹ ×83¹ ×C1₁¹ *c2′ Xc3) = ( 1400,300,0,0,0,1400,800,0,0 |x) Determine the cost (in dollars) of the production schedule. Total = $ 3910 X
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