$2.(30$ points$)$ Colour Company Ltd manufactures interior and exterior wall paints by mixing M$1$ and M$2$ raw materials. The basics of the problem are given below.

Moreover, a market research has revealed that the daily demand for the interior paint is at least $3$ tons. The same research has found that daily demand for the exterior paint is at least $2$ tons. Formulate the Lirnear Programming Model which maximizes the daily profit of Color Company Ltd