Let $p + q = 10$, where $p$, $q$ are integers. Value-I = Maximum value of $p imes q$ when $p$, $q$ are positive integers. Value-II = Maximum value of $p imes q$ when $p \ge -6$, $q \ge -4$. Which one of the following is correct?

Question

Let $p + q = 10$, where $p$, $q$ are integers. Value-I = Maximum value of $p 	imes q$ when $p$, $q$ are positive integers. Value-II = Maximum value of $p 	imes q$ when $p \ge -6$, $q \ge -4$. Which one of the following is correct?

Aicharya · Accepted Answer

With $p+q=10$, the product $pq$ is maximised when $p$ and $q$ are as close as possible. Value-I: positive integers, $p=q=5$ gives $pq = 25$. Value-II: $p\ge-6$, $q\ge-4$ with $p+q=10$; the unconstrained maximum is again at $p=q=5$ (which satisfies $5\ge-6$ and $5\ge-4$), giving $pq = 25$. So Value-I = Value-II = 25. Answer (c).

Let $p + q = 10$, where $p$, $q$ are integers. Value-I = Maximum value of $p \times q$ when $p$, $q$ are…

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