A furniture manufacturer produces tables and chairs
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
A furniture manufacturer produces tables and chairs. The profit on a table is Rs 350 and on a chair is Rs 120. Production conditions for the coming week are as follows:
• Wood available: at most 60 board-units. A table uses 6 board-units and a chair uses 2 board-units.
• Skilled labour available: at most 40 hours. A table needs 4 hours and a chair needs 1 hour.
• Demand restriction: the company must manufacture at least twice as many chairs as tables.
Answer the questions below.
(i) Formulate the optimisation problem, clearly defining variables, writing the objective to be maximised and all constraints including non-negativity.
(ii) Draw the feasible region on a graph, mark every vertex (corner point) and list their coordinates.
(iii) Using your diagram, determine the weekly production plan that maximises profit and state the maximum profit obtained.