Excel Solver Linear Programming: Simplex LP Models That Work
Build Excel Solver linear programming models with SUMPRODUCT objectives, linear constraints, and the Simplex LP engine—plus infeasibility fixes.
Keep models linear so Simplex LP can prove optimality.
Excel solver linear programming is the workhorse layer of spreadsheet optimization: linear objective, linear constraints, Simplex LP engine. When your model stays linear, Solver returns solutions you can defend in class or operations reviews. When you sneak nonlinear logic into cells, Simplex LP is the wrong tool—and may fail silently if you pick the wrong engine.
See the Excel Solver example template guide for workbook packaging. This article focuses on keeping models linear and letting Simplex LP do its job.
Key takeaway: Express objectives and constraints with SUMPRODUCT sums of variables, avoid nonlinear functions of variables, select Simplex LP, and treat infeasibility as a constraint conflict—not a bug.
Recognize a linear program on a sheet
Decision variables are quantities—units, hours, dollars. The objective is a weighted sum such as:
=SUMPRODUCT(profit_range, quantity_range)
Each constraint compares another weighted sum to a limit:
=SUMPRODUCT(hours_per_unit, quantity_range) <= available_hours
No variable squared, no variable multiplied by another variable, no IF that routes based on a variable's value. Microsoft's product-mix with Solver example stays in this territory.
Build the LP table
[TABLE: Block | Role | Example content | Objective row | Total profit SUMPRODUCT | Resource rows | LHS SUMPRODUCT <= capacity | Demand rows | Individual variable <= market limit]
Label each constraint row. Use separate cells for left-hand side and limit so the Solver dialog references clear addresses. Our how to use Solver walkthrough shows dialog wiring.
List variables → write linear objective → write each constraint formula → verify linearity → select Simplex LP → Solve
Simplex LP versus wrong engines
Simplex LP applies the simplex algorithm family to linear programs. Frontline's optimization methods guide contrasts Simplex LP with GRG Nonlinear and Evolutionary. If your model is LP and you choose GRG, you may get a feasible point without knowing it is globally optimal.
Warning: Piecewise linear approximations still count as nonlinear if implemented with variable-dependent IF. Use segment variables with extra constraints if you truly need piecewise structure.
Integer and binary constraints
Sometimes quantities must be whole units. After adding a constraint, choose int for integers or bin for zero-one decisions. Solve time can grow, but structure stays linear in the relaxation. Document integrality so readers know why runtime increased.
Product highlight: A readable LP template separates data (coefficients) from formulas (SUMPRODUCT) so you can swap scenarios without rebuilding Solver references.
Diagnose infeasibility and unboundedness
Infeasible means conflicting limits—demand minimum above capacity maximum, for example. Relax one constraint at a time to find the conflict. Unbounded means the objective can improve forever while constraints stay satisfied—often a missing upper bound on variables.
Sensitivity reports (when enabled) show shadow prices: how much the objective would improve if a binding constraint relaxed slightly. Teach readers to interpret shadow prices only within allowable ranges reported on the sheet.
Classroom product-mix alignment
The classic two- or three-product model fits LP perfectly. Coefficients live in tables; formulas stay visible. Students learn sensitivity by editing profits and rerunning Solve. For a full numeric narrative, continue to Excel Solver example: product-mix walkthrough.
When to leave pure LP
If your model needs diminishing returns curves, fixed-charge logic, or nonlinear efficiency, acknowledge the departure and switch engines per our optimization methods article. Do not mislabel a nonlinear sheet as a Simplex LP demo.
The PlanoNest Excel Solver Example1 template centers on a linear Simplex LP demonstration with onboarding—available as a one-time purchase with instant digital download; confirm details on the product page. Browse planner templates for adjacent planning workbooks.
Shadow prices and allowable increases
When Excel provides sensitivity output, shadow prices describe how much the objective would improve if a binding constraint relaxed by one unit, within an allowable range. Teach students to read those ranges: beyond them, different constraints become binding and the shadow price changes.
If sensitivity reports are disabled in a classroom build, you can still discuss binding constraints from the Answer report. A capacity row at its limit with slack of zero is the narrative equivalent for beginners.
Formulating LP from word problems
Translate English limits into algebra before touching cells. "At most 120 labor hours" becomes <= 120. "At least 10 chairs" becomes a variable lower bound or >= 10 constraint. "Exactly 500 units total" is equality. Mis-encoded inequalities are the top reason feasible regions look empty.
Practice with two products before three. Two-variable models can even be sketched on paper so students see why a corner solution wins in LP.
Non-negativity and upper bounds
Decision variables often require >= 0 constraints. Without them, a maximization model might allocate negative "production," which is mathematically optimal but nonsense operationally. Upper bounds—maximum campaign spend, warehouse slots—also matter; unbounded variables can cause unbounded objectives.
Document every bound in the Start Here sheet if you distribute the file. Reviewers should not hunt for hidden limits on auxiliary tabs.
Handoff note
Before handing off the sheet, replace example coefficients with clearly marked test values and ask another person to reproduce one objective total manually. That review catches mislabeled constraints, locked variable cells, and wrong changing-cell ranges faster than trusting the Solver status line alone.
Treat Solver reports as calculated outputs, not standalone evidence. Keep the workbook, engine choice, assumption date, and coefficient table together. If profits or capacities change later, create a new dated scenario instead of silently replacing numbers behind a report already shared with stakeholders.
Archive one solved workbook per month if you use Solver for planning. Future you will need to explain why March's mix differed from February's when commodity prices moved. A short changelog tab beats reconstructing decisions from email threads.
If students or colleagues fear Solver, remind them it only adjusts cells you permit. You remain in control of every formula and limit; Solver searches within the fence you built.
Before handing off the sheet, replace example coefficients with clearly marked test values and ask another person to reproduce one objective total manually. That review catches mislabeled constraints, locked variable cells, and wrong changing-cell ranges faster than trusting the Solver status line alone.
Treat Solver reports as calculated outputs, not standalone evidence. Keep the workbook, engine choice, assumption date, and coefficient table together. If profits or capacities change later, create a new dated scenario instead of silently replacing numbers behind a report already shared with stakeholders.
Archive one solved workbook per month if you use Solver for planning. Future you will need to explain why March's mix differed from February's when commodity prices moved. A short changelog tab beats reconstructing decisions from email threads.
If students or colleagues fear Solver, remind them it only adjusts cells you permit. You remain in control of every formula and limit; Solver searches within the fence you built.
Before handing off the sheet, replace example coefficients with clearly marked test values and ask another person to reproduce one objective total manually. That review catches mislabeled constraints, locked variable cells, and wrong changing-cell ranges faster than trusting the Solver status line alone.
Treat Solver reports as calculated outputs, not standalone evidence. Keep the workbook, engine choice, assumption date, and coefficient table together. If profits or capacities change later, create a new dated scenario instead of silently replacing numbers behind a report already shared with stakeholders.
Archive one solved workbook per month if you use Solver for planning. Future you will need to explain why March's mix differed from February's when commodity prices moved. A short changelog tab beats reconstructing decisions from email threads.
Frequently asked questions
What makes a model linear in Excel Solver?
Each constraint and the objective must be linear in the decision variables—no products of variables, no variable exponents, no variable inside IF branches.
When should I select Simplex LP?
Select Simplex LP when the model is linear and you want reliable global optimality for LP problems.
Why use SUMPRODUCT in LP models?
SUMPRODUCT expresses weighted sums of variables—profit, resource usage, or material totals—in one formula Solver can evaluate efficiently.
What does infeasible mean in Simplex LP?
No set of variable values satisfies all constraints simultaneously. Relax or fix conflicting limits.
Can Simplex LP handle integers?
Use the int or bin constraint types for integer programming; Excel may switch to a branch-and-bound approach within Simplex LP selections.
About the author
PlanoNest Editorial prepares practical Excel and planning template guides for the PlanoNest blog.
Disclosure: PlanoNest sells digital Excel, Google Sheets, and Notion templates. Links to PlanoNest products and collections point to our own template shop.
