A workshop manufactures tables and chairs each working day
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
A workshop manufactures tables and chairs each working day. The daily production is governed by the following constraints:
• Each table requires 4 hours of woodworking and 2 hours of assembly.
• Each chair requires 2 hours of woodworking and 1 hour of assembly.
• The workshop can provide at most 40 hours of woodworking and at most 16 hours of assembly per day.
• At least 3 tables must be produced daily due to advance orders.
• Non-negativity restrictions apply.
Let x represent the number of tables and y represent the number of chairs produced daily.
(a) Translate all the above information into a system of linear inequalities in x and y.
(b) For each inequality, draw its boundary line on the coordinate plane, specify whether the line is solid or dashed, and, using a suitable test point, identify the correct half-plane to be shaded.
(c) Determine and clearly shade the feasible region that satisfies all constraints.
(d) List the coordinates of every vertex of the feasible region obtained in part (c).