Maximise the linear objective over the feasible region.

01 / Standard#Your turn

3x+4y\le7,\quad x-2y\ge-1,\quad y\ge-1,\quad z=3x+y

Official paper · jm01-2025 · I.14 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use the first constraint to bound 3x+y.

Hint 2

Then use y≥−1 and test attainability.

Worked solution

Eliminate x from an upper bound for the objective.
$3x+y\le7-3y\le10$
Both bounds attain equality at a feasible point.
$(x,y)=\left(\frac{11}3,-1\right),\quad x-2y=\frac{17}3\ge-1$

D: maximum 10.

Checks and common pitfalls: An upper bound is a maximum only after a feasible equality case is found.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Eliminate x from an upper bound for the objective.
$3x+y\le7-3y\le10$
Both bounds attain equality at a feasible point.
$(x,y)=\left(\frac{11}3,-1\right),\quad x-2y=\frac{17}3\ge-1$

Think first. Reveal a hint when the class is ready.

2025 JM01