Home › JEE Main › Mathematics › Linear Programming › If an optimum does exist on an unbounded region,…
If an optimum does exist on an unbounded region, where must it occur?
AAt a casual point
BAt a corner point
CAt a central point
DAt a curved point
Answer & Solution
Correct answer: B. At a corner point
1. Unboundedness threatens whether an optimum exists at all.
2. It does not change where one would have to sit if it does.
3. If it exists, it must occur at a corner point of the region.
4. The corner point theorem still applies.
_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: