$(5$ points$)$ Weenies and Buns is a food processing plant that manufactures buns and frankfurters for hot dogs. They grind their own flour for the buns at a maximum rate of $200$ pounds per week. Each bun requires $0\mathrm{.}1$ pound of flour. They currently have a contract with Pigland, Inc., which specifies that a delivery of $800$ pounds of pork product is delivered every Monday. Each frankfurter requires $\frac{1}{4}$ pound of pork product. All the other ingredients in the buns and frankfurters are in plentiful supply. Finally, the labor force at Weenies and Buns consists of five employees working full time $(40$ hours per week each$).$ Each bun requires two minutes of labor, and each frankfurter requires three minutes of labor. Each bun yields a profit of $$0\mathrm{.}20,$ and each frankfurter yields a profit of $$0\mathrm{.}40.$

Weenies and Buns would like to know how many buns and how many frankfurters they should produce each week so as to achieve the highest possible profit. Please formulate the linear programming model algebraically.