Master Linear Programming with Excel’s Solver in Just 15 Minutes!

Introduction:
Ever felt overwhelmed with optimizing decisions in business or personal projects? Linear programming is here to help! In a mere 15 minutes, you can learn how to harness the power of Excel’s Solver tool to tackle these problems head-on.

Quick Scenario:
You run a small factory producing two bestsellers: A and B. But here’s the catch: you have limited resources. Your goal? To figure out how many of each product to produce to maximize your profit

Example:

Suppose you run a manufacturing business, and you want to maximize profits for two products: A and B.

• Product A’s profit margin is $5 per unit, and Product B’s profit margin is $7 per unit.
• Product A requires 2 hours of labor and 3 square feet of material.
• Product B requires 4 hours of labor and 1 square foot of material.
• You have 16 hours of labor and 8 square feet of material available.

Objective: Determine how many units of Product A and B you should produce to maximize profit.

Steps:

1. Set Up Your Spreadsheet:
   • Cell A1: “Product A”
   • Cell B1: “Product B”
   • Cell A2: Enter “0” (this will be your variable for Product A’s production quantity)
   • Cell B2: Enter “0” (variable for Product B’s production quantity)
   • Cell D1: “Profit per Unit”
   • Cell D2: 5
   • Cell D3: 7
   • Cell E1: “Total Profit”
   • Cell E2: =D2*A2 + D3*B2
2. Input Constraints:
   • Cell A4: “Hours of labor used”
   • Cell A5: “Material used”
   • Cell B4: =2*A2 + 4*B2
   • Cell B5: =3*A2 + B2
   • Cell C4: “≤ 16”
   • Cell C5: “≤ 8”
3. Open Solver:
   • Go to the Data tab.
   • Click on “Solver” in the Analysis group (If you don’t see Solver, you might need to install it).
4. Set the Objective:
   • Set Objective: E2
   • Equal to: Max
5. Set the Variables:
   • By Changing Variable Cells: A2, B2
6. Set the Constraints:
   • Add:
     • Cell Reference: B4, constraint: ≤ 16
     • Cell Reference: B5, constraint: ≤ 8
7. Choose a Solving Method:
   • Select “Simplex LP” (Linear Programming).
8. Solve:
   • Click “Solve” and Excel will find the optimal solution.
9. Review the Solution:
   • Excel will display the solution in the variable cells (A2, B2) and the maximum profit in E2.
10. Implement/Interpret:

• Based on the numbers provided in A2 and B2, you’ll know the number of units of Product A and B to produce to maximize profit given the constraints.

Note: Make sure your linear relationship assumptions and constraints are correct, as Solver will rely on these to find the best solution.

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