For the LPP 'Maximise Z = 3x + 5y subject to x + y ≤ 8, x + 3y ≤ 12, x ≥ 0, y ≥ 0', name its objective function, constraints and non-negative restrictions. Test whether (4, 2) and (6, 3) are feasible, and find Z where possible.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Write what is given and what is to be found. Given: the LPP. To find: its parts, and whether (4, 2) and (6, 3) satisfy all the constraints.
2 · Write the rule. A point is feasible only if it satisfies every constraint, including x ≥ 0, y ≥ 0.
3 · Name the parts.
Objective function: Z = 3x + 5y (maximise)
Constraints: x + y ≤ 8, x + 3y ≤ 12
Non-negative restrictions: x ≥ 0, y ≥ 0
4 · Test (4, 2).
4 + 2 = 6 ≤ 8, true
4 + 6 = 10 ≤ 12, true
Feasible. Z = 12 + 10 = 22
5 · Test (6, 3).
6 + 3 = 9 ≤ 8, false
Not feasible, so Z is not needed
6 · Check and box the answer. (4, 2) is feasible with Z = 22; (6, 3) is not feasible.
Scoring tip: Test every constraint for each point. One broken constraint makes the point infeasible.
