题目
OPMGT 301 C Test Your Knowledge: Linear Programming
多重下拉选择题
Consider a resource-allocation problem with the following data: Activity 1 Activity 2 Activity 3 Profit per unit $50 $40 $70 Resource Type Resource Usage (units) per Unit of Activity Resource Available (units) Activity 1 Activity 2 Activity 3 A 30 20 0 500 B 0 10 40 600 C 20 20 30 1000 Formulate a spreadsheet model for this problem, then use Solver to solve and determine the optimal solution that maximizes the total profit given the resource availability above. Note: You do NOT have to include the integer constraints in the model. The optimal solution is to pursue [ Select ] 16.667 8.667 18.667 units of Activity 1, [ Select ] 0 5.333 8.333 units of Activity 2, and [ Select ] 15 13.667 17.333 units of Activity 3. The maximum profit is $ [ Select ] 1883.333 2050.667 1780.333 .
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标准答案
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思路分析
Question restatement:
- We are given a resource-allocation problem with three activities, each having a profit per unit and resource usage per unit across three resource types A, B, and C. The available amounts of resources are A=500, B=600, C=1000. The goal is to formulate a model and solve to maximize total profit (integer constraints not required).
- The provided result fields (dropdowns) are:
1) Units of Activity 1: 16.667
2) Units of Activity 2: 0
3) Units of Activity 3: 13.667
4) Maximum profit: 1883.333
Option-by-option analysis:
Option 1: “Units of Activity 1: 16.667”
- If we look at the resource A constraint, 30 units of A are consumed per unit of Activity 1. With 16.667 units of Activity 1, A usage is 30 × 16.667 ≈ 500 units, which exactly matches the available A. This suggests the A constraint is tight (binding) for this choice.
- The other resources would still need to accommodate Activity 3 (and any Activity 2 if present). In the given solution, Activity 3 is 13.667 units. The combination 16.667 of Activity 1 and 13.667 of Activity 3 uses B and C resources and should be checked for feasibility against B ≤ 600 and C ≤ 1000. A......Login to view full explanation登录即可查看完整答案
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