**Linear Programming Homework Answers**

Those who thought Linear Programming was easy to comprehend, ask a management student and you will know the answer for sure. A mathematical approach for augmenting or minimizing a linear function to know the output or cost is what linear programming is all about. If I had to put in a common manâ€™s words, linear programming is one of the ways to perform optimization problems by making assumptions.

The topic is vast for sure, and when it comes to **linear programming homework answers**, the subject becomes all the more heated.

Study of this topic is difficult to understand. There are several of factors and features that affect the linear programming. Before we head towards the factors and features, it is important to know,

**WHAT IS LINEAR PROGRAMMING?**

- In this, the optimum points are found with the help of linear functions to come up with answers for depicted complex situations.
- It is one of the important topics while learning data science.
- For instance, suppose you want to go to the down town, and the GPS shows high traffic. In this case, the linear programming in personal life is implemented. You will find which the shortest route is so that you can reach the place on time.

**Points to note: **

There are various terms that are associated with Linear Programming too. Let us have a one to one association with it.

**Decision variable:**It states the solution to it. This is a variable that decides the output of the decision.**Objective Function**__:__it is here where the objectives of decision making are done.**Constraints:**The restrictions and limitations are looked while taking decision.**Non-negativity restriction**__:__It is a must that to take decision variables for linear programs, non-negative values must be taken into consideration.**Operation research**__:__Here the way one gives an approach towards a decision making to operate an arrangement involving various methods

There are various problems that students have to deal while taking into account. This is the reason why it is necessary that the pupils are well versed with the terminologies of the topic.

**Steps in order to formulate a linear programming problem**

- Identifying the decision variables
- Writing down of objective function
- Taking the constraints into consideration
- Stating the non-negativity restrictions
- To see if all the above are on par with linear functions

**For instance;**

In a pizza company, the delivery boy has 3 deliveries to do. The Pizza Company being situated at a point Z and the delivery locations being A, B, and C, now here the question is, the pizza delivery boy is looking for the shortest route to cover all the three destinations so that he can save time and fuel too.

The pizza delivery boy has to calculate the routes in order to find the shortest route which can save time and fuel too. This process is called the Operation Research. Now the routes cannot be in a straight line but will have turns. However, taking with assumptions, the problem is dealt with ease. This is called real life Linear Programming phenomena.

Now let us look from a mathematical model point of view. It is here where the students require **linear programming homework answers**

There are various ways of coming up with solutions for linear programming problems such as

- Formulating A Problem
- With Graphical Methods
- Using Open solver
- Simplex Method
- Northwest Corner Method
- Least Cost Method

For example, on a farm, there is production of Sugarcane and rice. The owner of the farm wants to know how to plant the above plantations in 220 hectares of field with a budget of $20,000 and man days available 2,400 with the following details

Variety |
Cost (Price/Hec) |
Net Profit (Price/Hec) |
Man-days/Hec |

Sugarcane | 200 | 100 | 20 |

Rice | 400 | 240 | 60 |

#### How to solve this problem now,

We follow the steps

**Step 1: Identifying the decision variables: here the decisions variables are the total area required for growing sugarcane and rice, letâ€™s say P and Q respectively.**

P and Q are the decision variables.

The next step being writing down the objective functions

Here, the farmer wishes to earn $100 for sugarcane and $240 for rice for each hectare. This is the objective functions here.**Max P = 100P + 240Q**

Now coming to the constraints

- With a budget of $20,000 the entire production has to be done, so the equation becomes

200P + 400Q **â‰¤ 20,000**

**Coming to the man days constraints which are 2400 man days, the equation comes to 20P + 60Q â‰¤ 2400****The last constraint being the total area which is 220 hectares, the equation to that would be P +Q â‰¤ 220**

Step 4 consist of the non-negative restriction

**Here the** values P and Q will be greater than or equal to 0. This goes without saying.

**PÂ â‰¥ 0, QÂ â‰¥ 0**

Once the entire linear program is aligned, solving the equations is again a task with the various ways it can be done. This is though time-consuming.

**Role**** of online services: **

Now let us understand what role does **linear programming homework answers **service providers play?

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