Linear Programming: Addressing Common Problem Terminologies with Their Solutions

  Assignment Help   17th Mar 2021

Linear programming problems consist of a linear function to be extended or reduced. Linear Programming is a process of implementing optimization that is applied to achieve the best outcome in a mathematical model. In linear programming, the objective function (the linear function outlining the measures to be maximized or minimized) and the restrictions (the method of equations or variations explaining the constraints on the decision variables) are interpreted by the linear relations. With linear programming assignment help you deal with the common problem terminologies of Linear Programming.

However, in this blog, we are going to address them further. Want to know more about them? Let’s get into them.

What Are The Terminologies for Linear Programming Problems?

Here are the terminologies that you should be familiar with before getting started with linear programming problems:

Objective Function: It refers to some numerical value that must be extended or reduced. For instance, if you are connected with some sort of business, then it obvious that your primary goal will always be to find ways to maximize profits and minimize loss.

Constraints: The constraints refer to the restrictions of the decision variables. For instance, if you have a business, then the budget, space, number of employees, production potential, etc. will be the limitations.

Decision Variables: Decision variables can be defined as the variables that determine the output. For instance, you are a farmer who aims to produce wheat and barley, then estimating the overall area for producing wheat and barley will be the decision variables.

Non-negativity Restriction: Non-negativity restriction implies that the decision variable values should be higher than or equivalent to 0. The students can ask for programming assignment help to gain more information about this.

How to Describe a Linear Programming Problem?

For a problem to be described as a linear programming problem, all the constraints, objective function, and decision variables should be linear functions. Here are the steps you have to follow for defining a problem as a linear programming problem:

  • Recognize the number of decision variables
  • Distinguish the restrictions on the decision variables
  • Note down the objective function as a linear equation
  • Explicitly assert the non-negativity constraint
  • Linear Programming Problems

A linear programming problem deals with a linear function to be extended or reduced subject to specific limitations in the design of linear equations or variations.

Solved Example for You

Question 1: You need to buy some filing cabinets. You know that Cabinet X costs $10 per unit, requires six square feet of floor space, and holds eight cubic feet of files. Cabinet Y costs $20 per unit, requires eight square feet of floor space, and holds twelve cubic feet of files. You have been given $140 for this purchase, though you don’t have to spend that much. The office has room for no more than 72 square feet of cabinets. How many of which model should you buy, in order to maximize storage volume? Write the maximum storage volume in the provided box.

  • 0
  • 100
  • 200
  • 300

Answer: Let the number of X models be x and let the number of Y models be y,

For floor 6x + 8y = 72

 or 3x + 4y = 36

10x +20y ≤ 140

Volume = 8x + 12y

Now x + 2y ≤ 14

 Hence 2x + 4y ≤ 14

Volume = 8x + 12y = 8x +108 – 9x = 108 – x

2x + 4y ≤ 28

 2x + 36 – 3x ≤ 28

 x ≥ 8

So volume is maximum when x is minimum, x = 8. Hence, maximum volume = 108 – 8 = 100.

Do You Need Linear Programming Assignment Help?

If you are facing any kind of trouble with the linear programming assignments then without having any second thoughts reach out to the experts of BookMyEssay. Their experts offer assignment help online to the students who have hard time solving the linear programming problems. For more details contact today!


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