A small factory has two products (A and B). In order to keep the factory running, at least 20+k units of products must be produced each day where k is the largest digit of your student number. Product A costs $200 to produce, while Product B costs $100 to produce. The total costs must be less than $8000 as the budget each day. In addition, the market regulations require that the number of Product B cannot exceed twice the number of Product A, but must be at least more than half the number of Product A. If each Product A gives a profit of $40 and each Product B gives a profit of $60, design a simple daily production portfolio (in terms of the numbers of Products A and B to be produced) so that the total profit is maximized. • Write this problem as a simple linear programming problem with the objective and all appropriate constraints. • Find its optimal solution by solving it using two different methods (e. g., graphical method and Excel Solver/Matlab).