Corner points of the feasible region for an LPP are: (0, 3), (5, 0), (7, 6), (8, 0) and (0, 4). Let Z = 3x + 7y be the objective function. Then, the value of (Max Z - Min Z) is:
Answer & explanation
Correct answer: option 4
$\text{Given corner points: }(0,3),(5,0),(7,6),(8,0),(0,4).$
$Z=3x+7y.$
$Z(0,3)=3(0)+7(3)=21.$
$Z(5,0)=3(5)+7(0)=15.$
$Z(7,6)=3(7)+7(6)=21+42=63.$
$Z(8,0)=3(8)+7(0)=24.$
$Z(0,4)=3(0)+7(4)=28.$
$\text{Maximum }Z=63,\;\text{Minimum }Z=15.$
$\text{Max }Z-\text{Min }Z=63-15=48.$
$\text{Required value}=48.$