Consider the feasible set in fig a find an objective functio

Consider the feasible set in fig (a) find an objective function of the from ax t by that has greatest value at the given point.

from the graph we take the objective function as

F=8x+3y and the values of F are

at (0,9) F=8(0)+3(9)=0+27=27

at (3,8) F=8(3)+3(8)=24+24=48

at (8,3) F=8(8)+3(3)=64+9=73

at (9,0) F=8(9)+3(0)=72+0=72

therefore we see that F is maximum value 73 at (8,3)

hence F=8x+3y is an required objective function.