A unit makes school bags and lunch bags. A school bag needs 3 hours on machine I and 1 hour on machine II. A lunch bag needs 1 hour on machine I and 2 hours on machine II. Machine I runs at most 15 hours a day and machine II at most 10 hours. The profit is ₹ 80 on a school bag and ₹ 100 on a lunch bag (example rates). Formulate this as an LPP to maximise profit.
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: machine hours for each bag, the daily limits and the profits. To find: the LPP.
2 · Define the decision variables. Let x = number of school bags and y = number of lunch bags made each day.
3 · Write the rule. An LPP has an objective function, one constraint for each limit, and x ≥ 0, y ≥ 0.
4 · Write the objective function. Profit Z = 80x + 100y, to be maximised.
5 · Write the constraints.
Machine I: 3x + y ≤ 15
Machine II: x + 2y ≤ 10
Non-negative: x ≥ 0, y ≥ 0
6 · Check and box the answer. Maximise Z = 80x + 100y subject to 3x + y ≤ 15, x + 2y ≤ 10, x ≥ 0, y ≥ 0. Check: x = y = 0 satisfies every limit.
Scoring tip: Write 'Let x = ...' in words. Undefined variables cost the first mark.
