$$zi$$ Ltd uses raw materials D$1$ and D$2$ to produce two domestic products; A and B$.$ The daily availabilities of raw materials D$1$ and D$2$ are $1500$ and $1450$ units, respectively. One unit of product A consumes $5$ unit of raw material D$1,$ and $6$ unit of raw material D$2.$ One unit of product B uses $4$ unit of raw material Di and $5$ unit of raw material D$2.$ The profits per unit of products A and B are $80$ TL and $60$ TL$,$ respectively. The daily demand for product A lies between $50$ and $200$ units,

that for product B between $60$ and $250$ units.

a$-$ Formulate the Linear programming model for this problem.

b$-$ Find the optimal product mix that maximize the total profit.