In the given figure, the feasible region of LPP is a parallelogram OABC. If the objective function is z = 3x + 4y, the maximum value of z is:

76

$\text{Vertices of parallelogram } OABC:$

$O(0,0),\;A(0,4),\;B(12,10),\;C(12,6).$

$z=3x+4y.$

$z(O)=3(0)+4(0)=0.$

$z(A)=3(0)+4(4)=16.$

$z(C)=3(12)+4(6)=36+24=60.$

$z(B)=3(12)+4(10)=36+40=76.$

$\text{Maximum value of } z = 76.$