Linear Programming Formulation problem faced - Maximization problem

In summary, the conversation discusses a scenario where Company Y produces two types of cookies, S and E, with limited supplies of ingredients. The objective is to develop a linear programming formulation to maximize revenue from the sales of both cookies. The solution provided by the individual includes defining variables for the sales of each type of cookie and setting constraints based on the percentage of ingredients required for each cookie.
  • #1
huiwangzi
1
0
Hi All.

I am new here and I faced some issues in formulating the objective functions and constraints for the following scenario.

Could any kind souls assist in giving me some advices on how I can proceed to do so?


Company Y is producing two different cookies; S cookies and E cookies. The ingredients of both cookies are Flour, Sugar and Chocolate (and nothing else). The company Y has the daily supply of 100KG of Flour, 20KG of Sugar and 30 KG of Chocolate. The mixture for Cookie S must contain at least 10% of Sugar and 10% of Chocolate. The mixture for Cookie E must contain at least 20% of Sugar. Cookie E are sold at \$25 per KG and Cookie S are sold at \$20 per KG. Develop an LP formulation for Company Y to maximise their revenue from the sales of both cookies. You may assume Company Y can sell as much as cookies that they can produce.

I have come out with the following answer. However, I am not too sure if it is correct. Appreciate if anyone could help me solve my queries.

Let X1 = Sales of Cookies S from Company Y
Let X2 = Sales of Cookies E from Company Y

Max 20 X1 + 25 X2
s.t. 0.10 X1 + 0.20 X2 ≤ 20
0.20 X1 ≤ 30 Thank you!
 
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  • #2
Managed to solve?
 

What is a "Linear Programming Formulation problem"?

A Linear Programming Formulation problem is a type of mathematical optimization problem where a linear objective function is maximized or minimized, subject to a set of linear constraints. It is used to find the best possible solution to a problem while considering various constraints and limitations.

What is meant by a "Maximization problem" in Linear Programming?

A maximization problem in Linear Programming is a type of optimization problem where the goal is to find the maximum value of a linear objective function, subject to a set of linear constraints. This means that the solution to the problem will be the best possible outcome that can be achieved while still adhering to the given constraints.

What are the key elements of a Linear Programming Formulation problem?

The key elements of a Linear Programming Formulation problem include:

  • Decision variables - these represent the quantities that can be manipulated in the problem.
  • Objective function - this is the function that is to be maximized or minimized.
  • Constraints - these represent the limitations or restrictions that must be adhered to while finding the solution.
  • Non-negativity constraints - these state that the decision variables must be greater than or equal to zero.

What are the steps involved in formulating a Linear Programming problem for maximization?

The steps involved in formulating a Linear Programming problem for maximization are:

  1. Identify the decision variables and define them.
  2. Write the objective function in terms of the decision variables.
  3. Define the constraints in terms of the decision variables.
  4. Make sure all decision variables have non-negativity constraints.
  5. Determine the feasible region by graphing the constraints.
  6. Determine the optimal solution by finding the point within the feasible region that maximizes the objective function.

What are some real-world applications of Linear Programming Formulation problems?

Linear Programming Formulation problems have a wide range of real-world applications, some of which include:

  • Resource allocation and production planning in businesses.
  • Scheduling and routing problems in transportation and logistics.
  • Portfolio optimization in finance and investments.
  • Diet planning in nutrition and healthcare.
  • Network flow optimization in telecommunications and computer networks.

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