Reflect upon a leader or manager who positively or negatively impacted your practice. Do not identify the leader by name. Describe the impact on your nursing practice.
Discuss the impact on the practice environment.
Analyze the individual’s leadership skills using either the American Association of Colleges of Nursing (AACN) or the American Organization for Nursing Leadership (AONL) leadership competencies provided.
Constraints:
Demand Constraints:
For Cable A: P_A+Q_A=60,000
For Cable B: P_B+Q_B=40,000
For Cable C: P_C+Q_C=120,000
Resource Constraints: Note: Available hours are converted to minutes by multiplying by 60.
Drawing: 0.1P_A+0.2P_B+0.1P_Cle24,000
Annealing: 0.1P_A+0.2P_B+0.2P_Cle36,000
Stranding: 0.1P_A+0.3P_B+0.3P_Cle48,000
Extrusion: 0.1P_A+0.3P_B+0.1P_Cle30,000
Assembly: 0.2P_A+0.1P_B+0.4P_Cle60,000
Non-negativity Constraints:
P_A,P_B,P_C,Q_A,Q_B,Q_Cge0
Based on the linear programming model, the optimal solution for minimizing total cost is to produce all of cables B and C in-house and to procure all of cable A.
Minimum cost attainable = $2,660,000
Decision variable values under optimal solutions:
Export to SheetsCable Type A B C Produce (feet) 0 40,000 120,000 Procure (feet) 60,000 0 0
Resource use:
Export to SheetsResource Available (minutes) Used (minutes) Not Used (minutes) Drawing 24,000 20,000 4,000 Annealing 36,000 32,000 4,000 Stranding 48,000 48,000 0 Extrusion 30,000 24,000 6,000 Assembly 60,000 52,000 8,000
(1) Cost decrease per additional hour and Maximum amount for additional hour
Export to SheetsResource Current availability (hours) Cost per hour Cost decrease per additional hour Maximum amount for additional hour Drawing 400 $60 $0 $60 Annealing 600 $240 $0 $240 Stranding 800 $180 $0.20 $180.20 Extrusion 500 $120 $0 $120 Assembly 1000 $300 $0 $300
Explanation: The "Cost decrease per additional hour" is known as the shadow price or dual value. It represents how much the total cost would decrease for each additional hour of a specific resource. In this case, only the Stranding resource is fully utilized (used 48,000 out of 48,000 minutes), making it a binding constraint. Therefore, its shadow price is non-zero, indicating that adding more of this resource would reduce the total cost. The other resources have surplus capacity, so an additional hour of any of them would not change the optimal solution or the total cost; their shadow prices are zero.
The "Maximum amount for additional hour" is the highest price the company should be willing to pay for an extra hour of a resource. This is the sum of the resource's existing cost per hour and its potential cost savings (the shadow price). For Stranding, the company should be willing to pay up to $180 (current cost) + $0.20 (potential saving) = $180.20 per hour.
(2) Impact of a price change for Cable C
If the purchase cost per foot of Cable C was $20 (instead of $15), the total minimum cost would increase by $6,000,000.
Decision Variables:
Let P_A, P_B, and P_C be the number of feet of cables A, B, and C produced in-house, respectively. Let Q_A, Q_B, and Q_C be the number of feet of cables A, B, and C procured from the outsourcing partner, respectively.
Objective Function:
Minimize the total cost, Z, which is the sum of in-house production costs and outsourcing costs. Z=6P_A+8P_B+10P_C+8Q_A+10Q_B+15Q_C