# How to Do Linear Programming in Excel (2 Suitable Ways)

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Linear Programming is one of the most interesting features of applied mathematics. We can solve linear programming through Excel. But Excel has no built-in function or feature to perform this. There are two ways to perform linear programming in Excel, and we will discuss them in detail here.

## What Is Linear Programming?

Linear programming is a mathematical term. It is a kind of modeling technique that can achieve the maximum profit or the minimum cost based on the relationships of a linear function. It is also called mathematical optimization.

## Introduction to Linear Programming Terms

We will discuss some basic terms of linear programming.

Decision Table: This table consists of some variables to determine the optimum solution to the problem.

Constraints: Those are the conditions imposed on the linear function to get the solutions.

Objective function: This function contains our objective. It is specified as quantitative.

Linearity: The relation between the variable must be linear.

Finiteness: The solution of all the variables must be finite.

Optimal Solution: This is the optimal point of our objective function. From this, we get the values of the variables.

## How to Do Linear Programming in Excel: 2 Suitable Ways

There are two ways to do linear programming on Excel. One is by using the graph, and another one is by using an Excel add-in. We will discuss both methods in detail in the next sections.

Suppose, we have the following objective function along with two constraints:

Function:

A=8X+10Y

Constraints:

2X+4Y<=72 and

4X+2Y<=48

### 1. Plot Graph to Do Linear Programming

Apply the following steps to solve the linear programming problem by plotting graph.

📌 Steps:

• First, we separate the coefficients of variables. • Now, we will find out the value of 2 variables considering the value of one variable 0 (Zero). See for the 1st constraint. When X is 36, Y becomes 0, and when Y is 0, X becomes 18.

Similarly, apply this to the 2nd constraint. Here, X=12 when Y=0 and Y=24 when X=0.

• Similarly, apply this to the 2nd constraint. Here, X=12 when Y=0 and Y=24 when X=0.

• Now, select the value from the 1st constraint.
• Click on the Insert tab.
• Choose the desired Scatter Chart from the Chart group. • We will see a graph based on the selection. • Now, keep the cursor on the chart and press the right button of the mouse.
• Choose Select Data from the Context Menu. • The Select Data Source window appears.
• Our input data is named Series1.
• We want to change the name.
• Select Series1 and click on the Edit option. • Put name C1 on the Series name box.
• After that, press OK. Values of the X and Y are taken from our selection.

• Now, we will add another source as we have another constraint.
• Click on the Add button. • Now, we will add another source as we have another constraint.
• Click on the Add button.
• The Edit series window appears.
• Put a name, and range for the values of X and variables.
• Again, press OK. • Again, press OK on the next window. • Look at the graph now. We have named the edge points.

• Based on the edge points, we form a new dataset table. We will now find out the position of the intersecting point using a formula. That is point C.

• Put the following formula on Cell E15.
`=MMULT(MINVERSE(C6:D7),F6:F7)` • Press the Enter We get the value of both X and Y coordinates. • Now, we will find out the optimal value using the formula below.
`=C15*\$C\$5+C16*\$D\$5` • Press Enter and drag the Fill Handle to the right side. We get different values of function A for different values of the variables.

At point C, we get the maximum value of A is 192, where X=4 and Y=16.

### 2. Linear Programming with Excel Add-In

In this section, we will use an Add-in named Solver for this linear system.

📌 Steps:

• First, we separate the coefficients in the following table. • Now, go to Cell E6 and put the following formula.
`=(\$C\$5*C6)+(\$D\$5*D6)` This formula will determine the result of function A.

• Look at the dataset.

As C5 and D5 are blank, the result is 0 (zero). We will expand the formula on Range E7:E8.

• Now, go to File >> Options >> Add-ins.
• Select the Solver Add-in from the list.
• Then, press Go.
• Check Solver Add-in and then press OK. • Now, click on Cell E6.
• Click on the Data tab.
• Then, click on the Solver option. • The Solver Parameters window appears.
• Input objects are marked on the image below.
• Set Objective is the cell we will apply the Solver.
• We want to get the maximum value, so check the Max option. Other options are also available.
• Then, press the Add button. • We consider those values are equal to or greater than 0. This indicated the value of X and Y. • This is for the given constraints value input.
• Finally, press OK. • Both constraints are shown here.
• Now, click on Solve button. • We get the values of the variable and the function A. ## Conclusion

In this article, we described how to do linear programming in Excel. We showed two methods graph and add-in with p[roper explanations. I hope this will satisfy your needs.

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