A company produces 3 types of cables: A, B, and C. In-house production costs per foot...

  

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A company produces 3 types of cables: A, B, and C. In-house production costs per foot of cables A, B, and C are $6, $8, and $10, respectively. The production process requires 5 resources: Drawing, Annealing, Stranding, Extrusion, and Assembly. For each resource, the table below specifies the number of minutes of the resource needed to produce a foot of each type of cable. For example, to produce each foot of Cable C, we need 0.1 minutes of Drawing, 0.2 minutes of Annealing, 0.3 minutes of Stranding, 0.1 minutes of Extrusion, and 0.4 minutes of Assembly. The column "Available hours", specifies the number of hours of each resource available during a production period. For the next production period the firm is contractually obligated to produce 60,000 feet of A, 40,000 feet of B, and 120,000 feet of C. Due to limited resource availability, these demands cannot be met by in-house production alone. The company must procure cables from an outsourcing partner, at higher costs, to meet the demand. The costs per foot for purchasing cables A, B, and C from the outsourcing partner are $8, $10, and $15, respectively. The production manager must decide how much of each type of cable to produce in-house and how much to purchase from the outsourcing partner to meet the demands at minimum cost. 0. Relevant data is summarized in the table below: Cable Type Demand (ft) Production Cost/ft Purchase Cost/ft Drawing (mins/ft) Annealing (mins/ft) Stranding (mins/ft) Extrusion (mins/ft) Assembly (mins/ft) A 60,000 $6 $8 0.1 0.1 0.1 0.1 0.2 B 40,000 $8 $10 0.2 0.2 0.3 0.3 0.1 C 120,000 $10 $15 0.1 0.2 0.3 0.1 0.4 Available hours 400 600 800 500 1000 Define the decision variables and specify the objective function and constraints. Decision Variables: XA, XB, XC: Number of feet of Cables A, B, and C produced. YA, YB, YC: Number of feet of Cables A, B, and C purchased. Objective Function: Our objective is to minimize total cost = cost of production + cost of purchase Minimize Cost = 6 XA + 8 XB + 10 XC + 8 yA + 10 yB+ 15 YC Constraints: I Number of feet of Cable A produced + Number of feet of Cable A purchased should be no less than the demand for Cable A. Demand A: XA + YA > 60000 Similarly, specify demand constraints for Cable B and Cable C. Demand B: XB + YB >= 40000 Demand C: XC + XC >= 120000 Number of minutes of Drawing used should not exceed the number of minutes available. Drawing availability: 0.1 xA + 0.2 xB+ 0.1 xC <- 24000 Similarly, specify availablility constraints for the other 4 resources. Annealing availability: 0.1 XA + 0.2 xB+ 0.2 xC <- 36000 Stranding availability: 0.1 xA+ 0.3 XB + 0.3 xC <- 48000 Extrusion availability: 0.1 XA + 0.3 xB + 0.1 xC <= 30000 Assembly availability: 0.2 XÃ + 0.1 xB + 0.4 XC <= 60000 All decision variables are non-negative. A company produces 3 types of cables: A, B, and C. In-house production costs per foot of cables A, B, and C are $6, $8, and $10, respectively. The production process requires 5 resources: Drawing, Annealing, Stranding, Extrusion, and Assembly. For each resource, the table below specifies the number of minutes of the resource needed to produce a foot of each type of cable. For example, to produce each foot of Cable C, we need 0.1 minutes of Drawing, 0.2 minutes of Annealing, 0.3 minutes of Stranding, 0.1 minutes of Extrusion, and 0.4 minutes of Assembly. The column "Available hours", specifies the number of hours of each resource available during a production period. For the next production period the firm is contractually obligated to produce 60,000 feet of A, 40,000 feet of B, and 120,000 feet of C. Due to limited resource availability, these demands cannot be met by in-house production alone. The company must procure cables from an outsourcing partner, at higher costs, to meet the demand. The costs per foot for purchasing cables A, B, and C from the outsourcing partner are $8, $10, and $15, respectively. The production manager must decide how much of each type of cable to produce in-house and how much to purchase from the outsourcing partner to meet the demands at minimum cost. 0. Relevant data is summarized in the table below: Cable Type Demand (ft) Production Cost/ft Purchase Cost/ft Drawing (mins/ft) Annealing (mins/ft) Stranding (mins/ft) Extrusion (mins/ft) Assembly (mins/ft) A 60,000 $6 $8 0.1 0.1 0.1 0.1 0.2 B 40,000 $8 $10 0.2 0.2 0.3 0.3 0.1 C 120,000 $10 $15 0.1 0.2 0.3 0.1 0.4 Available hours 400 600 800 500 1000 Define the decision variables and specify the objective function and constraints. Decision Variables: XA, XB, XC: Number of feet of Cables A, B, and C produced. YA, YB, YC: Number of feet of Cables A, B, and C purchased. Objective Function: Our objective is to minimize total cost = cost of production + cost of purchase Minimize Cost = 6 XA + 8 XB + 10 XC + 8 yA + 10 yB+ 15 YC Constraints: I Number of feet of Cable A produced + Number of feet of Cable A purchased should be no less than the demand for Cable A. Demand A: XA + YA > 60000 Similarly, specify demand constraints for Cable B and Cable C. Demand B: XB + YB >= 40000 Demand C: XC + XC >= 120000 Number of minutes of Drawing used should not exceed the number of minutes available. Drawing availability: 0.1 xA + 0.2 xB+ 0.1 xC <- 24000 Similarly, specify availablility constraints for the other 4 resources. Annealing availability: 0.1 XA + 0.2 xB+ 0.2 xC <- 36000 Stranding availability: 0.1 xA+ 0.3 XB + 0.3 xC <- 48000 Extrusion availability: 0.1 XA + 0.3 xB + 0.1 xC <= 30000 Assembly availability: 0.2 XÃ + 0.1 xB + 0.4 XC <= 60000 All decision variables are non-negative.

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Decision Variables As mentioned in question refer to the Gl quantities of cables to be p... View the full answer