Simplex Method Application

This repository provides a practical solution to the Knapsack Problem using Python and the simplex method. The Knapsack Problem is a well-known combinatorial optimization challenge often encountered in logistics and resource allocation scenarios. It involves selecting a combination of items from a set, each with its weight and value, to maximize the total value while adhering to a constraint, such as a maximum weight or volume.

Knapsack Problem:

1. Problem Context:

A large electronics company is relocating from Brazil to Portugal and needs to move its assets to the new facilities. The company has hired container shipments to transport furniture and equipment. After sending the shipments, there is some leftover space in the containers with a weight capacity of 500 kg and a volume of 830 m3. In this case, it would be beneficial to fill this space with items available in the company's inventory, as the entire inventory cannot be shipped.

2. Problem Data:

Item	Unit	Weight (unit)	Volume (unit)	Quantity in Stock
1	Static Actuator	Box	0.7	4.5
2	Rotational Actuator	Box	1.7	2.1
3	Pneumatic Actuator	Box	0.1	3.7
4	Galvanized T-Base	Package	0.8	4.7
5	Butterfly Valve	Package	0.9	1.4
6	Slide Switch	Package	2.2	3.6
7	Key Switch	Package	3.8	2.5
8	Inverter	Box	3.6	2.4
9	7-Way Harness	Box	2.2	4.9
10	4-Way Harness	Box	2.8	2.8
11	Double Switch	Box	0.1	3.6
12	Inverter Switch	Box	1.4	3.6
13	Ignition Switch	Box	3.4	2.1
14	Split Valve	Package	1.1	2.2
15	Monobloc Valve	Package	3.2	1.3
16	Expansion Joint	Box	2.7	2.1
17	Galvanized X-Base	Package	3.9	3.1
18	Micro Router	Box	1.3	1.1
19	Micro Switch	Box	1.6	3.1
20	2-Axis Terminal	Package	1.6	1.2
21	4-Axis Terminal	Package	0.5	2.3
22	6-Axis Terminal	Package	0.3	1.7
23	Pressure Sensor	Box	1.2	3.8
24	Proximity Sensor	Box	1.1	1.3
25	Flexinity	Package	1.2	1.3
26	Flexinity Mini	Package	3.6	4.3
27	Oscillator	Box	0.8	2.3
28	Timer	Box	1.1	3.6
29	Thermistor	Box	3.6	2.6
30	Slide Potentiometer	Box	2.2	3.2