From the below-mentioned graph of shaded feasible region of a linear programming problem (LPP) with objective function $z=1.50 x + 1.00 y$, the maximum value of $z$ will be;-
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 52.5
$Z=1.5x+1.0y.$
$\text{Corner points of shaded feasible region from graph:}$
$A(0,40),\;B(15,30),\;C(20,20),\;D(20,0).$
$Z(A)=1.5(0)+1(40)=40.$
$Z(B)=1.5(15)+1(30)=22.5+30=52.5.$
$Z(C)=1.5(20)+1(20)=30+20=50.$
$Z(D)=1.5(20)+1(0)=30.$
$\text{Maximum value occurs at }B(15,30).$
$Z_{\max}=52.5.$