Company ABC is a known exporter of two local products X and Y$.$ The company would like to maximize its profit. How many of each product should it produce to maximize profit? Every unit of product X can be sold at $$10$ and product Y at $$20.$ The daily demand is limited to at most $200$ units of product X and $300$ for product Y$.$ The current workforce of $10$ people can produce a total of at most $500$ units per day.

$1.$ Formulate an LP model.

$2.$ Manually calculate to find the feasible region. Provide a detailed calculation and a visualization.

$3.$ Validate the calculations using Excel Solver.