The maximum value of the objective function $Z = 10x + 15y$ of an L.P.P, subjected to the constraints $2x + 4y ≤ 8, 3x + y ≤6, -x-y≥-4, x≥0, y ≥ 0$ is:

34

The correct answer is Option (4) → 34

$Z=10x+15y.$

$2x+4y\le8 \Rightarrow x+2y\le4.$

$3x+y\le6.$

$-x-y\ge-4 \Rightarrow x+y\le4.$

$x\ge0,\;y\ge0.$

$\text{Corner points of feasible region:}$

$(0,0).$

$(2,0)\;(\text{from }3x+y=6,\;y=0).$

$(0,2)\;(\text{from }x+2y=4).$

$(1.6,1.2)\;(\text{intersection of }x+2y=4 \text{ and }3x+y=6).$

$Z(0,0)=0.$

$Z(2,0)=20.$

$Z(0,2)=30.$

$Z(1.6,1.2)=10(1.6)+15(1.2)=34.$

$\text{Maximum value of }Z=34.$