Corner points of the feasible region for LPP are : (4, 0), (0, 5), (7, 0), (5, 2) and (0, 3). Let Z=3x + 6y be the objective function. Then, the value of (Max z- Min Z) is :
Answer & explanation
Correct answer: option 3
$\text{Given corner points: }(4,0),(0,5),(7,0),(5,2),(0,3).$
$Z=3x+6y.$
$Z(4,0)=3(4)+6(0)=12.$
$Z(0,5)=3(0)+6(5)=30.$
$Z(7,0)=3(7)+6(0)=21.$
$Z(5,2)=3(5)+6(2)=15+12=27.$
$Z(0,3)=3(0)+6(3)=18.$
$\text{Maximum }Z=30,\;\text{Minimum }Z=12.$
$\text{Max }Z-\text{Min }Z=30-12=18.$
$\text{Required value}=18.$