A linear programming problem (LPP) along eith the graph of its co… - Vidyadip

MCQ

A linear programming problem (LPP) along eith the graph of its constraints is shown below.The correspondig objective function is :Z = 18x + 10y which has to be minimized. The smallest value of the objective function Z is 134 and is obtained at the corner point (3,8).

The optimal solution of the above linear programming problem_______________.

A
does not exist as the feasible region is unbounded.
B
does not exist as the inequality 18x + 10y < 134 does not have any point in common with the feasible region.
C
exists as the inequality 18x + 10y > 134 has infinitely many points in common with the feasible region.
D
exists as the inequality 18x + 10y < 134 does not have any point in common with the feasible region.

✓

Answer

Since the inequality Z = 18x + 10y < 134 has no point in common with the feasible region hence the minimum value of the objective function Z = 18x + 10y is 134 at P(3,8).

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