Furniture dealer: feasible region OABCफ़र्नीचर व्यापारी: सुसंगत क्षेत्र OABCFurniture dealer: feasible region OABC

NCERT Fig 12.1 · Class 12 Maths · Chapter 12 · interactive diagram

Parts and what they mean

• Feasible region OABC (सुसंगत क्षेत्र OABC) — The common region of ALL the constraints (including x ≥ 0, y ≥ 0). Every point in it, or on its boundary, is a feasible solution.
• Investment line 5x + y = 100 (निवेश रेखा 5x + y = 100) — From 2500x + 500y ≤ 50000 (divide by 500). Allowed side: below the line.
• Storage line x + y = 60 (संग्रहण रेखा x + y = 60) — At most 60 pieces can be stored. Allowed side: below the line.
• Corner O(0, 0) (कोनीय बिंदु O(0, 0)) — Buy nothing: Z = 0.
• Corner A(20, 0) (कोनीय बिंदु A(20, 0)) — Only 20 tables (all the money): Z = 250 × 20 = 5000.
• Corner B(10, 50) — maximum (कोनीय बिंदु B(10, 50) — अधिकतम) — Where 5x + y = 100 meets x + y = 60: 10 tables, 50 chairs, Z = 2500 + 3750 = 6250 (the maximum).
• Corner C(0, 60) (कोनीय बिंदु C(0, 60)) — Only 60 chairs (storage is full): Z = 75 × 60 = 4500.
• Infeasible point (25, 40) (असुसंगत बिंदु (25, 40)) — 5(25) + 40 = 165 > 100 and 25 + 40 = 65 > 60: outside the region — an infeasible solution.
• x-axis (x-अक्ष) — The horizontal number line; inputs x are read here.
• y-axis (y-अक्ष) — The vertical number line; outputs y = f(x) are read here.
• Origin O(0, 0) (मूल बिंदु O(0, 0)) — Where the two axes cross.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 12.1. Report a mistake