Production Planning - Handbook

Type: LP (Linear Programming)

This handbook explains the Production Planning sample problem in the LP Black Box platform.

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The Problem

Scenario

A factory produces three products (P1, P2, P3) with different profits and resource requirements.

Product	Profit ($)	Labor (hrs)	Materials (units)	Machine (hrs)
P1	45	2	3	1
P2	30	1.5	2	2
P3	25	1	1.5	1.5

Your Goal

Maximize total profit while respecting resource limits.

The Constraints

1. Labor: Max 100 hours available

   Formula: 2×P1 + 1.5×P2 + 1×P3 ≤ 100

2. Materials: Max 120 units available

   Formula: 3×P1 + 2×P2 + 1.5×P3 ≤ 120

3. Machine Time: Max 80 hours available

   Formula: 1×P1 + 2×P2 + 1.5×P3 ≤ 80

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How to Use

Step 1: Load the Sample

Select Production Planning from the dropdown.

Step 2: Examine the Problem

Variables: P1, P2, P3 (Continuous, lower_bound=0)

Objective: Maximize profit (P1=45, P2=30, P3=25)

Constraints: labor ≤ 100, materials ≤ 120, machine ≤ 80

Step 3: Solve

The solver determines how many of each product to produce for maximum profit.

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Try It Yourself

• What if P3 becomes more profitable (change coefficient to 35)?
• Add a minimum production requirement for P1

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This sample demonstrates multi-product profit maximization with multiple resource constraints.