Questions
OPMGT 301 C Test Your Knowledge: Linear Programming
Multiple dropdown selections
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 .
View Explanation
Verified Answer
Please login to view
Step-by-Step Analysis
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 explanationLog in for full answers
We've collected over 50,000 authentic exam questions and detailed explanations from around the globe. Log in now and get instant access to the answers!
Similar Questions
Solving a linear program can never result in integer values for the decision variables.
Consider the following optimization problem and the constraint boundary lines given below. Maximize profit = 4X + 4Y Constraints 3X + 2Y ≤ 150 X - 2Y ≤ 10 2X + 3Y ≤150 X, Y ≥ 0 If we increase the objective function coefficient of x by 2, i.e., 4 becomes 6, the new optimal solution includes point C.
Consider the following optimization problem and the constraint boundary lines given below. Maximize profit = 4X + 4Y Constraints 3X + 2Y ≤ 150 X - 2Y ≤ 10 2X + 3Y ≤150 X, Y ≥ 0 When the constraint coefficient of x in the blue constraint changes from 1 to 3, the optimal solution changes.
Consider the following Excel sensitivity report and it's accompanying problem: Minimize cost = X + 2Y subject to X + 3Y ≥ 90 8X + 2Y ≥ 160 3X + 2Y ≥120 Y ≤ 70 X, Y≥ 0 Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$3 X 25.71 0 1 2 0.333333333 $C$3 Y 21.43 0 2 1 1.333333333 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $J$6 LHS 90 0.57 90 62 50 $J$7 LHS 248.57 0 160 88.57142857 1E+30 $J$8 LHS 120 0.14 120 150 28.18181818 $J$9 LHS 21.43 0 70 1E+30 48.57142857 Suppose we add another variable, x3, with an objective function coefficient of 9, and constraint coefficients of 8, 3, and 5 for the first three constraints, respectively. What is the marginal impact of this new variable on the objective function? (In your calculations round all the numbers to 2 decimals.)
More Practical Tools for Students Powered by AI Study Helper
Making Your Study Simpler
Join us and instantly unlock extensive past papers & exclusive solutions to get a head start on your studies!