CUET · MATHS · PYQ PAPER 2023
Corner points of the feasible region for a linear programming program are \((0,2),(3,0),(4,1),(2,3)\) and \((0,3)\).
Let \(F=4 x+6 y\) be the objective function.
The minimum value of \(F\) occurs at :
- A \((0,2)\) only
- B \((3,0)\) only
- C mid point of the line segment joining the points \((0,2)\) and \((3,0)\) only
- D every point on the line segment joining the points \((0,2)\) and \((3,0)\)
Answer & Solution
Correct Answer
(D) every point on the line segment joining the points \((0,2)\) and \((3,0)\)
Step-by-step Solution
Detailed explanation
\(F(0,2) = 4(0) + 6(2) = 12\) \(F(3,0) = 4(3) + 6(0) = 12\) \(F(4,1) = 4(4) + 6(1) = 22\) \(F(2,3) = 4(2) + 6(3) = 26\) \(F(0,3) = 4(0) + 6(3) = 18\) Minimum value is \(12\). The minimum value occurs at every point on the line segment joining the points \((0,2)\) and \((3,0)\).
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