Home › JEE Main › Mathematics › Linear Programming › If the feasible region is unbounded, a maximum o…
If the feasible region is unbounded, a maximum or minimum value:
AMay not exist
BMust always exist
CMust be negative
DMay be duplicated
Answer & Solution
Correct answer: A. May not exist
1. An unbounded region stretches away without limit in some direction.
2. The objective function may simply keep growing along it.
3. If the region is unbounded, a maximum or minimum may not exist.
4. So existence has to be checked rather than assumed.
_Source: NCERT Class XII Mathematics Part II, Ch 12 'Linear Programming'_
Related questions
Two depots hold 180 and 250 tons; two customers order 200 and 150 tons. After the cheapestA gardener needs AT LEAST 10 units of chemical A. A jar gives 5 units and a carton 1 unit.A gardener needs at least 10, 12 and 12 units of chemicals A, B and C. Jars cost 3,000 andMine A gives 1, 3 and 5 tons of high, medium and low grade ore daily; mine B gives 2 tons Profit is Shs. 3000 on a ring and Shs. 1900 on a chain. With $x$ rings and $y$ chains, theA firm makes $x$ rings and $y$ chains, at most 24 items a day. A ring takes 1 hour, a chaiSome problems minimise a linear function subject to given:A linear programming problem must have constraints that are: