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"What's the optimal solution to this linear programmingproblem?Max2X + 3Ys.t.  4X +   9Y ≤ 7210X + 11Y ≤ 11017X +   9Y ≤ 153          X,Y ≥ 0  Answer:  We have,Max2X + 3Ys.t.  4X +   9Y ≤ 7210X + 11Y ≤ 11017X +   9Y ≤ 153          X,Y ≥ 0To convert the problem to canonical form we will add addingslack variable to each constraint as all constraints areof  type '≤'After introducing slack variablesMax2X + 3Y+0S1 +0S2 + 0S3s.t.  4X +   9Y + S1≤ 7210X + 11Y + S2 ≤ 11017X +   9Y +S3 ≤ 153          X,Y ≥ 0Iteration-1Cj23000BCBXBXYS1S2S3Min RatioXB / YS10724(9)10072 /9=8→S201101011010110 /11=10S30153179001153 /9=17Z=0Zj00000Zj-Cj-2-3↑000Negative minimum Zj-Cj is -3 and its columnindex is 2. So, the entering variable is Y.Minimum ratio is 8 and its row index is 1. So, the leaving basisvariable is S1.∴ The pivot element is 9.Iteration-2Cj23000BCBXBXYS1S2S3Min RatioXB / XY380.444410.1111008 / 0.4444 = 18S2022(5.1111)0-1.22221022 / 5.1111 = 4.3043→S3081130-10181 / 13 = 6.2308Z=24Zj1.333330.333300Zj-Cj-0.6667↑00.333300Negative minimum Zj-Cj is -0.6667 and itscolumn index is 1. So, the entering variable is X.Minimum ratio is 4.3043 and its row index is 2. So, the leavingbasis variable is S2.∴ The pivot element is 5.1111.Iteration-3Cj23000BCBXBXYS1S2S3Min RatioY36.087010.2174-0.0870X24.304310-0.23910.19570S3025.0435002.1087-2.54351Z=26.8696Zj230.17390.13040Zj-Cj000.17390.13040Since all Zj-Cj≥0Hence, the optimal solution is:X=4.3043,Y=6.087Max Z=26.8696"
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