Why a corner? Iso-profit lines Z = 250x + 75yकोनीय बिंदु ही क्यों? समान-लाभ रेखाएँ Z = 250x + 75yCorner hi kyon? Iso-profit lines Z = 250x + 75y

NCERT Extra (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.
• Line 250x + 75y = 2500 (रेखा 250x + 75y = 2500) — Every point on it gives the same profit Rs 2500. It cuts through the region, so we can do better.
• Line 250x + 75y = 4500 (रेखा 250x + 75y = 4500) — Passes through C(0, 60); still cuts the region.
• Line 250x + 75y = 6250 — last touch (रेखा 250x + 75y = 6250 — अंतिम स्पर्श) — The farthest parallel line that still touches the region; it touches only at the corner B(10, 50). So the maximum is 6250 at B.
• Line 250x + 75y = 7500 (रेखा 250x + 75y = 7500) — Misses the region completely: a profit of 7500 is impossible.
• Direction in which Z increases (Z के बढ़ने की दिशा) — Moving the line this way (parallel to itself) increases Z = 250x + 75y.
• Corner B(10, 50) (कोनीय बिंदु B(10, 50)) — Optimal solution: 10 tables and 50 chairs, profit Rs 6250.
• 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 Extra (Fig 12.1). Report a mistake