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A problem has the rules x + 2y ≤ 6 and 2x + y ≥ 14, with x ≥ 0 and y ≥ 0…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A problem has the rules $x + 2y \le 6$ and $2x + y \ge 14$ , with $x \ge 0$ and $y \ge 0$ . First find the largest value of $2x + y$ over the region $x + 2y \le 6$ , $x \ge 0$ , $y \ge 0$ . Then say how many feasible points the problem has.

Need a reminder? The key ideaShow

If the rules clash, there is no feasible solution. If the lines $Z = k$ are parallel to an edge, both corners of that edge, and every point between them, give the optimal value. linprog minimises, so negate $Z$ to maximise and turn $\ge$ rules round by multiplying by $-1$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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