Determine whether the problem has multiple solutions, unbounded solutions, or no feasible solutions.Maximize z = 10x1 + 11x2 + 7x3, subject to2x1 + 3x2 − 9x3 ≤ 722x1 + 5x2 − 10x3 ≥ 100x1 ≥ 0, x2 ≥ 0, x3 ≥ 0The problem has multiple solutions.The problem has unbounded solutions. The problem has no feasible solutions.

An iterative algorithm for resolving linear programming (LP) problems is the simplex method. It functions by first providing a feasible solution to the LP problem, which is then improved upon iteratively until an optimal solution is obtained. This algorithm is frequently utilized in many different fields, such as business, engineering, and finance, and it is well-liked and efficient.Given LP-Max Z = 10x1 + 11x2 + 7x3Subject to -2x1 + 3x2 - 9x3 <= 722x1 + 5x2 - 10x3 >= 100x1, x2, x3 >= 0First, change this LP into canonical form-Here, constraint 1 has <= sign, so we add slack variable x4and constraint 2 has >= sign, so we subtract surplus x5 and add artificial variable x6Max Z = 10x1 + 11x2 + 7x3 + 0x4 + 0x5 - 0Mx4Subject to -2x1+ 3x2 - 9x3 +x4 = 722x1+ 5x2 -1 0x3 -x5 +x6 = 100x1, x2, x3, x4, x5, x6 >= 0Iteration 1: BCbPx1x2x3x4x5x6Q1011700-Mx407223-910024x6-M10025-100-1120Max-100M-2M-10-5M-1110M-70M0Here, the entering variable is x2 and the leaving basis variable is x6. Thus the pivot element is 5.Iteration 2: BCbPx1x2x3x4x5x6Q1011700-Mx40120.80-310.6-0.624x211200.41-30-0.20.220Max220-5.60-290-2.2M+2.2Here, the entering variable is x3 but we find that all the coefficients in the x3 column are negative or zero.Thus, x3 can not be entered into the basis.Therefore, the solution to the given problem is considered as unboundedTherefore-the correct option is (b) The problem has an unbounded solution