$2.$ Yingfei Co$.$ plans to produce products A and B$.$ It is known that the unit product profits of products A and B are $$8$ and $$10$ respectively. Some raw materials are required for product production. The production of each product also needs to go through two workshops of the factory. The raw materials and processing time required in each workshop and the total resources are shown in the table below.

How many pieces of these two products should the company manufacture every day in order to maximize the company's profits?

Define the decision variables and formulate a linear programming $($LP$)$ model foi this problem $(20$ scores$).$ Furthermore, write the standard form of the LP model$(1$ scores$),$ use simplex method in tabular form to solve the problem and give out