The correct answer is Option 1: A, B, C only
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A. If R is unbounded then a max./min. value may not exist (Correct): When the feasible region extends infinitely in a certain direction, the objective function can also increase or decrease indefinitely. In such cases, a finite maximum or minimum value might not be reachable.
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B. If R is bounded then a max. and min. value will always exist (Correct): This is a key property of LPP. If the feasible region is a closed, bounded polygon (a compact set), the objective function must attain both a maximum and a minimum value within that region.
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C. If a solution exists, it must occur at a corner point (Correct): Known as the Corner Point Method, this principle states that the optimal value (maximum or minimum) of the objective function, if it exists, will always occur at one of the vertices (extreme points) of the feasible region.
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D. If R is bounded then max. will exist but min. may or may not exist (Incorrect): As stated in point B, if the region is bounded, both the maximum and the minimum are guaranteed to exist.
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