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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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