Question 9 8 pts Use the simplex method and the Duality Principle to solve the following minimum problem: Minimize: 3.21 + 8x2 Subject to the constraints: 2x1 + 7x2 > 9 X1 + 2x2 > 4 X1 > 0 X2 > 0 and using your final tableau answer the questions below by entering the correct answer in each blank box. Please enter fractions as 3/5, -4/7, and so on. P1 = 22 = C= Question 10 5 pts The following intermediate tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. S2 Py1 0 1 Y2 1 2 1 2 S1 1 2 0 RHS 3 2 1 2 0 0 1 1 0 -1 3 0 9 Find the pivot element(s) in the above tableau, and perform all the necessary pivot operations to obtain the final tableau. Then, using the final tableau, answer the following questions: The minimum function value is: The value of x1 in the minimum problem is : The value of x2 in the minimum problem is: Question 11 5 pts The following tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. P Y1 Y2 Si S2 RHS 0 1 2 1 0 6 0 1 6 0 1 3 1 -6 -18 0 0 0 Find the pivot element(s) in the above tableau, and perform all the necessary pivot operations to obtain the final tableau. Then, using the final tableau, the fol ving The minimum function value is: The value of Xi in the minimum problem is : The value of x2 in the minimum problem is: Question 12 5 pts The following intermediate tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. P Y2 $1 S2 RHS Yi 0 0 2 1 1 0 1 1 0 1 2 1 1 0 -2 0 3 2 3 Find the pivot element(s) in the above tableau, and perform all the necessary pivot operations to obtain the final tableau. Then, using the final tableau, answer the following questions: The minimum function value is: The value of x1 in the minimum problem is : The value of x2 in the minimum problem is