Example 1: maximise Z = 4x + yउदाहरण 1: Z = 4x + y का अधिकतमीकरणExample 1: Z = 4x + y maximise kijiye

NCERT Fig 12.2 · Class 12 Maths · Chapter 12 · interactive diagram

Parts and what they mean

• Feasible region OABC (bounded) (सुसंगत क्षेत्र OABC (परिबद्ध)) — 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 x + y = 50 (रेखा x + y = 50) — Boundary of x + y ≤ 50; feasible side is towards O.
• Line 3x + y = 90 (रेखा 3x + y = 90) — Boundary of 3x + y ≤ 90; feasible side is towards O.
• Corner O(0, 0) (कोनीय बिंदु O(0, 0)) — Z = 4(0) + 0 = 0.
• Corner A(30, 0) — maximum (कोनीय बिंदु A(30, 0) — अधिकतम) — Z = 4(30) + 0 = 120, the largest value. The region is bounded, so 120 is the maximum.
• Corner B(20, 30) (कोनीय बिंदु B(20, 30)) — Solve x + y = 50 and 3x + y = 90: 2x = 40, x = 20, y = 30. Z = 80 + 30 = 110.
• Corner C(0, 50) (कोनीय बिंदु C(0, 50)) — Z = 0 + 50 = 50.
• 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 12.2. Report a mistake