Write the equations and augmented matrix, and use your program to solve it.

A store has requested a manufacturer to produce pants and sports jackets.

For materials, the manufacturer has 750 m of cotton textile and 1,000 m of polyester. Every pair of pants (1 unit) needs 1 m of cotton and 2 m of polyester. Every jacket needs 1.5 m of cotton and 1 m of polyester.

The price of the pants is fixed at $50 and the jacket, $40.

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