Linear Programming Question 54
Question: $ z=ax+by,\ a,\ b $ being positive, under constraints $ y\ge 1 $ , $ x-4y+8\ge 0 $ , $ x,\ y\ge 0 $ has
Options:
A) Finite maximum
B) Finite minimum
C) An unbounded minimum solution
D) An unbounded maximum solution
Show Answer
Answer:
Correct Answer: B
Solution:
Given that both a and b are positive constants, the objective function is linear. Since the constraints include only non-negativity restrictions, the feasible region is bounded.
Thus, according to the Extreme Value Theorem, a continuous function on a closed interval (in this case, a bounded feasible region) attains its minimum and maximum values.
Hence, the correct answer is B) Finite minimum.
The solution is evident as the problem adheres to basic principles of linear programming in a bounded feasible region.
BETA
