Solving Linear Programming with Optimal 258

• maria69
In summary: Additionally, further optimization can be done by adjusting the constraints for protein and carbohydrate.
maria69
For the first part (i) i found the optimal solution when x1=180,x2=40 and the optimal is 258.
in (II) for the protein we have these 2 functions :PAx1+1.10x2 and 4x1+2x2=700
i found 2.2 and for cyrbohydrate with the functions :PAx1+1.10x2 and 3x1+x2=300
i found 3.3 so the first is 2.2<=PA<=3.3
For PB for the protein we have these 2 functions :1.50x1+PBx2 and 4x1+2x2=700
i found 0.75 and for cyrbohydrate with the functions: 1.50x1+PBx2 and 3x1+x2=300
i found 50. so the second is: 0.75<=PB<=50. AM I right?

For the (III) part for protein i have:4x1+2x2=701 and 3x1+x2=300
and i found that the shadow price is: £162.9
For the cyrbohydrate i have:4x1+2x2=700 and 3x1+x2=301 and i found

Can someone please check my answers and help me for the last part please?? I don't know how to write a memo. If someone please can do the first steps?
Thank you very much MARIA.

http://img19.imageshack.us/img19/894/oper3bv3.jpg

Last edited by a moderator:
Yes, your answers are correct. For the memo, you can start by stating the purpose of the memo and the problem that you are addressing. For example: This memo aims to address the optimal solution to the food rationing problem, with the objective of finding the optimal combination of protein (PA) and carbohydrate (PB) that meets the required nutrition levels while minimizing cost. Next, you can provide a brief background on how you derived the solution. This can include the equations and variables used, as well as the constraints. The solution was derived using linear programming, with x1 and x2 as the variables representing PA and PB respectively. The objective function is to minimize cost, which is equal to the sum of PA x1 + 1.10 x2 for protein, and PB x1 + 1.50 x2 for carbohydrate. The constraints are 4x1 + 2x2 = 700 for protein and 3x1 + x2 = 300 for carbohydrate. After this, you can provide the results of the solution. The optimal solution for x1 and x2 is 180 and 40 respectively. This yields an optimal cost of 258 and PA and PB values of 2.2 and 0.75 respectively. The shadow price for protein is £162.9 and for carbohydrate is £161.3. Finally, you can conclude your memo by summarizing the results and any actionable insights. In conclusion, the optimal solution is x1 = 180 and x2 = 40, with an optimal cost of 258. The corresponding values of PA and PB are 2.2 and 0.75 respectively. The shadow price for protein is £162.9 and for carbohydrate is £161.3. This suggests that the optimal solution should focus on minimizing protein intake, as the shadow price for protein is higher than that of carbohydrate.

1. What is linear programming?

Linear programming is a mathematical technique used to find the optimal solution to a problem with linear constraints. It involves maximizing or minimizing a linear objective function while satisfying a set of linear constraints.

2. How is linear programming used in real-world applications?

Linear programming has various applications in real-world problems, such as resource allocation, production planning, transportation, and financial planning. It is also commonly used in business and economics to optimize profits and minimize costs.

3. What is the optimal solution in linear programming?

The optimal solution in linear programming is the best possible solution that satisfies all the constraints and maximizes or minimizes the objective function. It is represented by a set of values for the decision variables that yield the highest or lowest value of the objective function.

4. What are decision variables in linear programming?

Decision variables are the unknown quantities that need to be determined in a linear programming problem. They represent the choices or decisions that need to be made to achieve the optimal solution.

5. What is the difference between feasible and infeasible solutions in linear programming?

A feasible solution in linear programming is one that satisfies all the constraints and can be considered as a candidate for the optimal solution. In contrast, an infeasible solution violates one or more constraints and is not a valid solution to the problem.

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