By XochitlW – Updated August 30, 2022

Linear programming lets you maximize or minimize an objective while satisfying a set of linear constraints. Microsoft Excel’s Solver add‑in turns this mathematical theory into a practical tool. This guide walks you through setting up and solving a standard‑form linear program in Excel, ensuring accuracy and confidence in your results.

Step 1: Prepare the Mathematical Model

Express your problem in the classic form:

Maximize c^Tx
Subject to Ax ≤ b, x ≥ 0

Where:

• c – coefficient vector for the objective function
• x – decision‑variable vector
• A – matrix of constraint coefficients
• b – right‑hand‑side vector

Before launching Solver, calculate each element of cTx, Ax, and b directly in Excel. It’s helpful to name the cells (e.g., Objective, X1, A1X1, B1) via Insert → Name → Define. Named ranges simplify the Solver interface and reduce errors.

Step 2: Enable and Launch Solver

1. Activate Solver – In Excel 2010+, go to File → Options → Add‑ins, check Solver Add‑in, and click OK. It will appear under the Data tab. 2. Open Solver – Click Data → Solver. 3. Define the Problem –

• Set Objective Cell: the cell containing your objective formula.
• By Changing Variable Cells: the cells that hold the decision variables (e.g., X1, X2).
• Add Constraints: For each row of A, click Add, select the corresponding cell, choose the inequality type (≤, ≥, =), and set the right‑hand‑side value.
• If all variables must be non‑negative, check Make Unconstrained Variables Non‑Negative.

Step 3: Choose the Solver Method

In the Select a Solving Method dropdown, choose Simplex LP for standard linear programs. For problems with nonlinear constraints, other methods are available, but Simplex is the default for linear models.

Step 4: Solve and Interpret Results

Click Solve. Solver will display a Solver Results dialog upon completion. Review the solution, then choose Keep Solver Solution to apply the optimal values to your worksheet, or Restore Original Values if the solution is unsatisfactory.

Quick Tips

• Double‑check your matrix calculations before launching Solver.
• Use named ranges to avoid reference errors.
• When in doubt, save a copy of your workbook before solving.

TL;DR

Set up your model, name key cells, and let Solver’s Simplex algorithm find the optimum.