Q.A furniture company manufactures tables and chairs. Each table needs 2 hours of carpentry and 1 hour of finishing; each chair needs 1 hour of carpentry and 3 hours of finishing. The factory has at most 100 hours of carpentry time and 120 hours of finishing time available per week. The profit is Rs 40 on each table and Rs 30 on each chair. Formulate this situation as a linear programming problem to maximise the total weekly profit.

Identify the two decision variables, write the profit as the objective function, and turn the two resource limits into $\le$ constraints, adding non-negativity.

Step 1 — decision variables. Let $x$ = number of tables made per week, $y$ = number of chairs made per week.

Step 2 — objective function. Each table earns Rs 40 profit and each chair Rs 30, so the total weekly profit is

which is to be MAXIMISED.

Step 3 — constraints. Each table needs 2 hours of carpentry and each chair needs 1 hour, with at most 100 hours of carpentry available:

Each table needs 1 hour of finishing and each chair needs 3 hours, with at most 120 hours of finishing available:

$x + 3y \le 120$ …

A common error is swapping which resource each product's coefficient belongs to (writing the carpentry constraint with the finishing hours, or vice versa) — always re-check each coefficient aga …