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A rancher is mixing two types of foods, Brand X and Brand Y, for his cattle. Each serving for cattle is required to have 360 grams of protein and 360 grams of fat. Brand X has 5 grams of protein and 10 grams of fat. Brand Y has 10 grams of protein and 5 grams of fat. Rancher has found that Brand X costs $3.5 and brand Y costs $5 per unit. Find out how much of each type should be used by the rancher to minimize cost. Keep in mind that the rancher has to buy at least one unit of each brand. Moreover, the number of brand X has to be twice the number of brand Y.

A rancher is mixing two types of foods, Brand X and Brand Y, for his cattle. Each serving for cattle is required to have 360 grams of protein and 360 grams of fat. Brand X has 5 grams of protein and 10 grams of fat. Brand Y has 10 grams of protein and 5 grams of fat. Rancher has found that Brand X costs $3.5 and brand Y costs $5 per unit. Find out how much of each type should be used by the rancher to minimize cost. Keep in mind that the rancher has to buy at least one unit of each brand. Moreover, the number of brand X has to be twice the number of brand Y.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 60P
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CAn you do this in Excel in the following template with Solver?

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  • A rancher is mixing two types of foods, Brand X and Brand Y, for his cattle. Each serving for cattle is required to have 360 grams of protein and 360 grams of fat. Brand X has 5 grams of protein and 10 grams of fat. Brand Y has 10 grams of protein and 5 grams of fat. Rancher has found that Brand X costs $3.5 and brand Y costs $5 per unit. Find out how much of each type should be used by the rancher to minimize cost.  Keep in mind that the rancher has to buy at least one unit of each brand.  Moreover,  the number of brand X has to be twice the number of brand Y.
Data      
       
       
       
       
       
       
       
       
       
       
       
       
Model      
       
Decision Variables    
       
       
       
       
       
       
Objective Function    
       
       
       
       
Constraints    
LS Relation RS [Name]
       
       
Expert Solution
Objective Functions and Constraints:

Objective Functions and Constraints:

                Based on the given details, the objective functions and constraints are 

Objective Function:

Min c = 3.5 x + 5 y  x – Brand X  y – Brand Y

Constraints:

                Subject to

Protein: 5 x + 10 y ≥ 360  Fat: 10 x + 5 y ≥ 360  At least one product: 1 x + 1 y ≥ 1  X has to be twice y: 2 x + y ≥ 1  x, y ≥ 0

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ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
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