Consider the following LP:Minimize1 2 2z = x + xSubject to − x1 + x2 =15 2x1 + x2  90 30 x2  x1, x2  0(a) Convert the LP given above to the standard form. Determine all the basic feasible solutions (bfs) of the problem. Give the values of both basic and nonbasic variables in each bfs.(b) Identify the adjacent basic feasible solutions of each extreme point of the feasible region. Using the graphical solution technique, solve the problem.(c) Using the big-M simplex method, find optimal solution.(d) Write the dual of the problem

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1. Consider the following LP: Minimize z = x, +2x2 Subject to -X, +x, =15 2x, +x, <90 x, 2 30 X,, X, 20 (a) Convert the LP given above to the standard form. Determine all the basic feasible solutions (bfs) of the problem. Give the values of both basic and nonbasic variables in each bfs. (b) Identify the adjacent basic feasible solutions of each extreme point of the feasible region. Using the graphical solution technique, solve the problem. (c) Using the big-M simplex method, find optimal solution. (d) Write the dual of the problem. 1. Consider the following LP: Minimize z = x, +2x2 Subject to -X, +x, =15 2x, +x, <90 x, 2 30 X,, X, 20 (a) Convert the LP given above to the standard form. Determine all the basic feasible solutions (bfs) of the problem. Give the values of both basic and nonbasic variables in each bfs. (b) Identify the adjacent basic feasible solutions of each extreme point of the feasible region. Using the graphical solution technique, solve the problem. (c) Using the big-M simplex method, find optimal solution. (d) Write the dual of the problem.