Consider the following optimization problem. Maximize Z=7x1 + 3x2 s.t. www x1 + 3/2 x2 12 2x1 + x2 15 x1 + x2 10 x1, x2 0 a. What type of optimization problem is this? (LP, MIP, IP, etc.) What does this mean about whether or not we can use the simplex method to solve this problem? b. What can we use as an initial BFS? c. Solve this problem using both the graphical solution and the simplex method in algebraic or tabular form. When you obtain the optimal solution, please clearly state what the optimal solution and objective function value are, as well as how you know the solution you obtained is optimal. d. How many simplex iterations did it take you to obtain the optimal solution?