Consider the LPP, with objective function optimize $Z=2x-y+5$ subject to constraints $3x+4y≤60; x+3y ≤ 30,x, y≥ 0$. If the corner points of feasible region are A(0,10), B(12, 6), C(20, 0) and O(0, 0), then
Match List I with List II
| List I | List II | ||
| A. | Minimum value of Z | I. | 45 |
| B. | Maximum value of Z | II. | 50 |
| C. | The sum of maximum and minimum value of Z | III. | -5 |
| D. | Maximum of Z - Minimum of Z | IV. | 40 |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 3
$Z=2x-y+5$
| points | value of Z | |
| (0, 10) | -5 (minimum) = Zmin | |
| (12, 6) | 23 | |
| (20, 0) | 45 (maximum) = Zmax | |
| (0, 0) | 5 |
Zmax = 45, Zmin = -5
Zmax - Zmin = 50, Zmax + Zmin = 40
order A - III, B - I, C - IV, D - II