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Instructions: Given the following problem statement: 1. Define the decision variables, objective function, and constraints as listed in the LP Model Formulation Steps section. Insert
Instructions: | |||||||
Given the following problem statement: | |||||||
1. Define the decision variables, objective function, and constraints as listed in the LP Model Formulation Steps section. Insert answers per guidance and highlight cell in light green. | |||||||
2. Use the results of the LP Model Formulation Steps to create an Objective Table and Constraint Table in the Results section. | |||||||
3. Solve the Linear Programming Problem using "Solver." | |||||||
4. Create a Answer Report. | |||||||
5. Create a Limits Report. | |||||||
6. Create a Limits Report. | |||||||
Variables | |||||||
Problem Statement | |||||||
The Holiday Meal Turkey Ranch is considering buying two different brands of turkey feed and blending them to provide a good, low-cost diet for its turkeys. Each feed contains, in varying proportions, some or all of the three nutritional ingredients essential for fattening turkeys. Each pound of brand 1 purchased, for example, contains 5 ounces of ingredient A, 4 ounces of ingredient B, and 0.5 ounce of ingredient C. Each pound of brand 2 contains 10 ounces of ingredient A, 3 ounces of ingredient B, but no ingredient C. The brand 1 feed costs the ranch $0.02 per pound, while brand 2 feed costs $0.03 per pound. Determine the lowest-cost diet that meets the minimum monthly intake requirement for each nutritional ingredient. | |||||||
Table 1. | |||||||
Product Resource Requirements | |||||||
Ingredient | Brand 1 Feed (B1) | Brand 2 Feed (B2) | Min Monthly Requirement per Turkey Oz | ||||
A | 5 | 10 | 90 | ||||
B | 4 | 3 | 48 | ||||
C | 0.5 | 0 | 1.5 | ||||
Cost per pound | $0.02 | $0.03 | |||||
LP Model Formulation Steps | |||||||
1. Define the decision variables - one variable per row. Format: Variable label = Variable name | |||||||
B1 = brand 1 | |||||||
B2 = brand 2 | |||||||
2. Define the objective function - Format: Max/Min = equation using variable labels and values | |||||||
Minimum Cost = 0.02*B1 + 0.03*B2 | |||||||
3. Define the constraints - one constraint per row. Provide a title for the constraint. Format = Title: equation | |||||||
INGREDIENT A: 5*B1 + 10*B2 >= 90 | |||||||
INGREDIENT B: 4*B1 + 3*B2 >= 48 | |||||||
INGREDIENT C: 0.5*B1 + 0*B2 >= 1.5 | |||||||
Results | |||||||
Objective Table | |||||||
Decision Variables | |||||||
B1 | B2 | Minimize | |||||
Objective Function | 0.02 | 0.03 | Cost | ||||
Pounds of feed | 8.4 | 4.8 | 0.312 | ||||
Constraints Table | |||||||
Cell Reference | See Table Above | Constraint | |||||
Constraint Variables | Technical Coefficients | LHS (units used) | Constraint Sign | RHS (constraint) | Slack (-) or Surplus (+) | ||
Ingredient A | 5 | 10 | 90 | >= | 90 | 0 | |
Ingredient B | 4 | 3 | 48 | >= | 48 | 0 | |
Ingredient C | 0.5 | 0 | 4.2 | >= | 1.5 | -2.7 | |
Answer Report | |||||||
Instructions | |||||||
1. Relabel the "Answer Report" tab to "Task 4_Answer Report" | |||||||
2. Place immediately after the "Task 4_MinAndReports" tab. | |||||||
Questions to interpret the results of the Answer Report | Type answer in the box | ||||||
1. What is the minimum cost? | 0.312 | ||||||
2. How many units of surplus are available for Ingredient C? | 0 | ||||||
3. How many units of slack are available for Ingredient C? | 2.7 | ||||||
4. Which ingredients are binding? | A&B | ||||||
5. Which ingredients are not binding? | C | ||||||
Sensitivity Report | |||||||
Instructions | |||||||
1. Relabel the "Sensitivity Report" tab to "Task 4_Sensitivity Report" | |||||||
2. Place immediately after the "Task 4_Answer Report" tab. | |||||||
Questions to interpret the results of the Sensitivity Report | Type answer in the box | ||||||
6. What is the allowable increase in B1's reduced cost? | 0.02 | ||||||
7. What is the allowable decrease in B2's reduced cost? | 0.005 | ||||||
8. What is B1's reduced cost? | 0 | ||||||
9. What is the allowable increase in ingredient C's shadow price? | 2.7 | ||||||
10. What is the allowable decrease in ingredient B's shadow price? | 13.5 | ||||||
11. What is ingredient A's shadow price? | 0.0024 | ||||||
Limits Report | |||||||
Instructions | |||||||
1. Relabel the "Limits Report" tab to "Task 4_Limits Report" | |||||||
2. Place immediately after the "Task 4_Sensitivity Report" tab. | |||||||
Questions to interpret the results of the Limits Report | Type answer in the box | ||||||
12. What is the lower limit for B1? | 8.4 | ||||||
13. What is the upper limit for B2? | N/A | ||||||
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