Use the simplex method to find the maximum value of P = 2x + y subject to these constraints. In order to correctly answer some of the following questions, you will need to use the method taught in the movies for choosing your pivot column. (If you do this problem correctly, all your answers will be whole numbers.) 5x + 14y = 420 8x + 8y = 312 17x + 5y = 459 x 0, y 0 (a) How many rows are there in your initial simplex tableau? 4 How many columns are there in your initial simplex tableau? 7 (b) At the end of your first complete step using the simplex method, the corner point of the solution region that corresponds to your simplex tableau is the point x = 26 X and y = 0 . At this corner point the value of P is 52 X. (Note: Since you have not yet finished pivoting this point does not represent the optimal solution.) (c) Complete any additional pivots needed to arrive at the optimal solution. Find the maximum value of P. P = 17 X This maximum value of P occurs when x = 61 X and y = 17