Problem 1 Suppose we have created a simplex tableau for a linear program (assuming it is a maximization problem) that looks like the following: Row 2 x1 x2 x3 x4 x5 x6 rhs 0 1 -20 0 0 80 0 0 240 1 01 0 1 00 0 3 2 0 -1 0 01 0 1 1 3 0 0 1010 0 3 4 0 1 0 0 1 1 0 2 (a) Based on the current tableau, write down the corresponding basic feasible solution. (b) The current tableau is clearly not optimal. To proceed to the next step, which variable will be chosen as the entering variable and which variable will be chosen as the leaving variable? (c) Write down the tableau that results from performing one simplex pivot/iteration based on your choice in part (b). Show your step-by-step work. (d) Is the solution indicated by your simplex tableau optimal after you finish part (c)? If so, write down the optimal solution and the optimal objective value. If not, identify the next entering variable and leaving variable.