Describe the operation of the simplex algorithm to implement a linear programming solution to the real world problem described below.

A store has requested a manufacturer to produce pants and sports jackets.The manufacturer has one week to fill the order. For materials, the manufacturer has 1,000m2 of cotton textile and 950m2 of polyester. Every pair of pants (1 unit) needs .5m2 of cotton and 2m2 of polyester. Every jacket needs 3m2 of cotton and 2m2 of polyester.

Each item produced must go through a final inspection process and the factory can only inspect a maximum of 500 units per week.

The price of the pants is fixed at $40 and the jacket at $75.

What is the number of pants and jackets that the manufacturer must give to the store so that these items obtain a maximum sale?