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Linear Programming EXERCISE 12.1 Solutions
- Q1: Solve the following Linear Programming Problems graphically: 1. Maximise $Z = 3x + 4y$ subject to the constraints : $x + y \leq 4$, $x \geq 0$, $y \geq 0$.
- Q2: Solve the following Linear Programming Problems graphically: 2. Minimise $Z = – 3x + 4y$ subject to $x + 2y \leq 8$, $3x + 2y \leq 12$, $x \geq 0$, $y \geq 0$.
- Q3: Solve the following Linear Programming Problems graphically: 3. Maximise $Z = 5x + 3y$ subject to $3x + 5y \leq 15$, $5x + 2y \leq 10$, $x \geq 0$, $y \geq 0$.
- Q4: Solve the following Linear Programming Problems graphically: 4. Minimise $Z = 3x + 5y$ such that $x + 3y \geq 3$, $x + y \geq 2$, $x, y \geq 0$.
- Q5: Solve the following Linear Programming Problems graphically: 5. Maximise $Z = 3x + 2y$ subject to $x + 2y \leq 10$, $3x + y \leq 15$, $x, y \geq 0$.
- Q6: Solve the following Linear Programming Problems graphically: 6. Minimise $Z = x + 2y$ subject to $2x + y \geq 3$, $x + 2y \geq 6$, $x, y \geq 0$. Show that the minimum of $Z$ occurs at more than two points.
- Q7: Solve the following Linear Programming Problems graphically: 7. Minimise and Maximise $Z = 5x + 10y$ subject to $x + 2y \leq 120$, $x + y \geq 60$, $x – 2y \geq 0$, $x, y \geq 0$.
- Q8: Solve the following Linear Programming Problems graphically: 8. Minimise and Maximise $Z = x + 2y$ subject to $x + 2y \geq 100$, $2x – y \leq 0$, $2x + y \leq 200$; $x, y \geq 0$.
- Q9: Solve the following Linear Programming Problems graphically: 9. Maximise $Z = – x + 2y$, subject to the constraints: $x \geq 3$, $x + y \geq 5$, $x + 2y \geq 6$, $y \geq 0$.
- Q10: Solve the following Linear Programming Problems graphically: 10. Maximise $Z = x + y$, subject to $x – y \leq –1$, $–x + y \leq 0$, $x, y \geq 0$.
Chapters in CBSE - Class 12 Mathematics
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