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Business Mathematics and Basic Statistics · Class 12 Commerce

Ch 17Linear Inequalities and Linear Programming — Class 12 Business Mathematics and Basic Statistics, concept-first.

Many business decisions are shaped not by an exact equation but by a limit — a budget that must not be exceeded, a production target that must be met, a machine that has only at most so many hours available in a week.

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Key concepts

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Graphing a Linear Inequality

A linear inequality in two variables, such as , is graphed in two steps: draw its boundary line using the line's two intercepts, then use a convenient test point (usually the origin) substituted into the original inequal…

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

1

Linear Inequalities in Two Variables — the Boundary Line and the Region

Many business decisions are shaped not by an exact equation but by a limit — a budget that must not be exceeded, a production target that must be met, a machine that has only at most so many hours ava…

2

Systems of Linear Inequalities and the Feasible Region

A real business problem is almost never governed by a single limit alone — a production plan is typically constrained by machine hours AND labour hours AND raw material, AND the plain fact that a quan…

3

Formulating a Linear Programming Problem

A linear programming problem (LPP) is a problem of finding the maximum or minimum value of a linear function, subject to a collection of linear constraints in the same variables, together with the non…

4

Solving an LPP by the Graphical (Corner-Point) Method

Once an LPP has been formulated and its feasible region graphed, the graphical method (also called the corner-point method) finds the optimal value of the objective function using a single remarkable…

More questions

10 Q
+Show 6 questions6 questions
  1. Example 1Graph the region represented by the linear inequality $2x + 3y \le 12$.Free
  2. Example 2Graph the region represented by the linear inequality $3x - y > 3$.Free
  3. Example 3Graph the system of linear inequalities $x + y \le 6$, $x \ge 0$, $y \ge 0$, and shade the feasible region.Preview
  4. Example 4A furniture company manufactures tables and chairs. Each table needs 2 hours of carpentry and 1 hour of finishing; each chair needs 1 hour o…Preview
  5. Example 5Solve the linear programming problem formulated in Worked Example 4 by the graphical (corner-point) method, and state the maximum profit.Preview
  6. Example 6A dietician wants to prepare a diet that provides at least 8 units of vitamin A and at least 10 units of vitamin B daily. Food $F_1$ costs R…Preview
+Show 4 questions4 questions
  1. Q7Graph the region represented by the linear inequality $4x + y \ge 4$.Free
  2. Q8Graph the system of linear inequalities $x + y \le 4$, $x \ge 0$, $y \ge 0$, and identify the feasible region.Free
  3. Q9A toy company manufactures two types of toys, A and B. Each toy A needs 2 hours of cutting and 1 hour of assembling; each toy B needs 1 hour…Preview
  4. Q10A farmer wants his crop to receive at least 10 units of nitrogen and at least 15 units of phosphorus. Fertiliser $P$ costs Rs 4 per bag and…Preview