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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
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 | |||||||
2. Define the objective function - Format: Max/Min = equation using variable labels and values | |||||||
3. Define the constraints - one constraint per row. Provide a title for the constraint. Format = Title: equation | |||||||
Results | |||||||
Objective Table | |||||||
Decision Variables | |||||||
Objective Function | |||||||
Constraints Table | |||||||
Cell Reference | See Table Above | Constraint | |||||
Constraint Variables | Technical Coefficients | LHS (units used) | Constraint Sign | RHS (constraint) | Slack (-) or Surplus (+) | ||
Questions to interpret the results of the Answer Report | Type answer in the box | ||||||
1. What is the minimum cost? | |||||||
2. How many units of surplus are available for Ingredient C? | |||||||
3. How many units of slack are available for Ingredient C? | |||||||
4. Which ingredients are binding? | |||||||
5. Which ingredients are not binding? | |||||||
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? | |||||||
7. What is the allowable decrease in B2's reduced cost? | |||||||
8. What is B1's reduced cost? | |||||||
9. What is the allowable increase in ingredient C's shadow price? | |||||||
10. What is the allowable decrease in ingredient B's shadow price? | |||||||
11. What is ingredient A's shadow price? | |||||||
Questions to interpret the results of the Limits Report | Type answer in the box | ||||||
12. What is the lower limit for B1? | |||||||
13. What is the upper limit for B2? |
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