Maximise Z = 6x + 4y subject to 3x + 2y ≤ 24, x ≤ 6, y ≤ 9, x ≥ 0 and y ≥ 0…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Maximise subject to , , , and . The corners are , , , and . Work out at each corner. Then find at the point , which lies on the edge between two corners.
Need a reminder? The key ideaShow
If the rules clash, there is no feasible solution. If the lines are parallel to an edge, both corners of that edge, and every point between them, give the optimal value. linprog minimises, so negate to maximise and turn rules round by multiplying by .
The worked solution
Have you tried it?
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.
Step 1. The values. At , . At , . At , . At , . At , .
Step 2. Compare. The maximum is , and it occurs at two corners, and .
Step 3. The edge. The point has , so it is on the edge between those corners. There .
Answer: the maximum is at corners, and at too. Every point of the edge is optimal, since on it.
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