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Question
Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px + qy, where p, q > 0. Condition on p and q so that the minimum of Z occurs at (3, 0) and (1, 1) is ______.
Options
p = 2q
p = `"q"/2`
p = 3q
p = q
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Solution
Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px + qy, where p, q > 0. Condition on p and q so that the minimum of Z occurs at (3, 0) and (1, 1) is `underlinebb(p = q/2)`.
Explanation:
| Corner points | Value of Z = px + qy; p, q > 0 |
| (0, 3) | Z = p(0) + q(3) = 3q |
| (1, 1) | Z = p(1) + q(1) = p + q |
| (3, 0) | Z = p(3) + q(0) = 3p |
So, condition of p and q
So that the minimum of Z occurs at (3, 0) and (1, 1) is p + q = 3p
⇒ p – 3p + q = 0
⇒ p = `"q"/2`.
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