The linear program is
Maximize:z=30x1+40x2+35x3Subjectto:3x1+4x2+2x3≤902x1+x2+2x3≤54x1+3x2+2x3≤43
with all variables non-negative.
Next we compute the optimal solution, to do this we put the linear program in standard form:
Maximize:z=30x1+40x2+35x3+0x4+0x5+0x6Subjectto:3x1+4x2+2x3+x4≤902x1+x2+2x3+x5≤54x1+3x2+2x3+x6≤43
with all variables non-negative.
Subsequently, we obtain our Tableau 1
x4(0)x5(0)x6(0)x130321−30x240413−40x335222−35x401000x500100x6000109054430
Next we locate the most negative number in the bottom row(-40). Then we compute ratios of positive numbers in our work column. Therefore our pivot element is 4. Using row reduction method, we reduce our pivot element to 1 and every other elements in the work column to 0, thereby generating Tableau 2.
x2(40)x5(0)x6(0)x13043454−50x2401000x335212321−15x40414−14−310x500100x600010245263251900
We notice there is still a negative element in the last row therefore repeating the process above we obtain Tableau 3.
x2(40)x3(35)x6(0)x13031653−5675x2401000x3350100x40316−13−2425x503−1323210x6000101221151215
Since there are no negative values in our last row. The solution is optimal. The optimal solution is x1=0,x2=40,x3=35,x4=0,x5=0,x6=0.
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