.
CHAPTER 12 STD 12 Date : 16/12/25
Linear Programming Maths
//X Section A
• Write the answer of the following questions. [Each carries 3 Marks] [36]
1. Solve the Linear Programming Problems graphically : Minimise Z = 3x + 5y
such that x + 3y > 3, x + y > 2, x, y > 0.
2. Solve the following linear programming problem graphically :
Maximise Z = 4x + y ...(1)
subject to the constraints :
x + y < 50 ...(2)
3x + y < 90 ...(3)
x > 0, y > 0 ...(4)
3. Solve the Linear Programming Problems graphically : Minimise Z = –3x + 4y
subject to x + 2y < 8, 3x + 2y < 12, x > 0, y > 0
4. Solve the following linear programming problem graphically :
Minimise Z = 200 x + 500 y ...(1)
subject to the constraints :
x + 2y > 10 ...(2)
3x + 4y < 24 ...(3)
x > 0, y > 0 ...(4)
5. Solve the following problem graphically :
Minimise and Maximise Z = 3x + 9y ...(1)
subject to the constraints : x + 3y < 60 ...(2)
x + y > 10 ...(3)
x < y ...(4)
x > 0, y > 0 ...(5)
6. Solve the following Linear Programming Problems graphically : Maximise Z = 3x + 2y
subject to x + 2y < 10, 3x + y < 15, x, y > 0
7. Solve the following Linear Programming Problems graphically : Maximise Z = 5x + 3y
subject to 3x + 5y < 15, 5x + 2y < 10, x > 0, y > 0
1.1.8) Lke[u
8. ykÃku÷ Mkwhu¾ ykÞkusLkLkku «&Lk yk÷u¾Lke heíku Wfu÷ku : z = 5x + 10y Lkwt ykÃku÷ þhíkkuLku yÄeLk {n¥k{ {qÕÞ íkÚkk LÞqLkík{
{qÕÞ {u¤ðku. x ³ 0, y ³ 0, x + y £ 50, 3x + y £ 90
9. Show that the minimum of Z occurs at more than two points : Maximise Z = – x + 2y, subject to the
constraints :
x > 3, x + y > 5, x + 2y > 6, y > 0.
10. Solve the following Linear Programming Problems graphically : Minimise Z = x + 2y
subject to 2x + y > 3, x + 2y > 6, x, y > 0
11. Solve the Linear Programming Problems graphically : Maximise Z = 3x + 4y
subject to the constraints : x + y < 4, x > 0, y > 0
12. Show that the minimum of Z occurs at more than two points : Minimise and Maximise Z = x + 2y
subject to x + 2y ³ 100, 2x – y £ 0, 2x + y £ 200, x, y ³ 0.
, .
CHAPTER 12 STD 12 Date : 16/12/25
Linear Programming Maths
Section [ A ] : 3 Marks Questions
No Ans Chap Sec Que Universal_QueId
1. - Chap 12 [Par... S1 4 QP25P11B1213_P2C12S1Q4
2. - Chap 12 [Par... S2 1 QP25P11B1213_P2C12S2Q1
3. - Chap 12 [Par... S1 2 QP25P11B1213_P2C12S1Q2
4. - Chap 12 [Par... S2 2 QP25P11B1213_P2C12S2Q2
5. - Chap 12 [Par... S2 3 QP25P11B1213_P2C12S2Q3
6. - Chap 12 [Par... S1 5 QP25P11B1213_P2C12S1Q5
7. - Chap 12 [Par... S1 3 QP25P11B1213_P2C12S1Q3
8. - Chap 12 [Par... S7 1.1.8 QP25P11B1213_P2C12S7Q1.1.8
9. - Chap 12 [Par... S1 9 QP25P11B1213_P2C12S1Q9
10. - Chap 12 [Par... S1 6 QP25P11B1213_P2C12S1Q6
11. - Chap 12 [Par... S1 1 QP25P11B1213_P2C12S1Q1
12. - Chap 12 [Par... S1 8 QP25P11B1213_P2C12S1Q8
Welcome To Future - Quantum Paper
CHAPTER 12 STD 12 Date : 16/12/25
Linear Programming Maths
//X Section A
• Write the answer of the following questions. [Each carries 3 Marks] [36]
1. Solve the Linear Programming Problems graphically : Minimise Z = 3x + 5y
such that x + 3y > 3, x + y > 2, x, y > 0.
2. Solve the following linear programming problem graphically :
Maximise Z = 4x + y ...(1)
subject to the constraints :
x + y < 50 ...(2)
3x + y < 90 ...(3)
x > 0, y > 0 ...(4)
3. Solve the Linear Programming Problems graphically : Minimise Z = –3x + 4y
subject to x + 2y < 8, 3x + 2y < 12, x > 0, y > 0
4. Solve the following linear programming problem graphically :
Minimise Z = 200 x + 500 y ...(1)
subject to the constraints :
x + 2y > 10 ...(2)
3x + 4y < 24 ...(3)
x > 0, y > 0 ...(4)
5. Solve the following problem graphically :
Minimise and Maximise Z = 3x + 9y ...(1)
subject to the constraints : x + 3y < 60 ...(2)
x + y > 10 ...(3)
x < y ...(4)
x > 0, y > 0 ...(5)
6. Solve the following Linear Programming Problems graphically : Maximise Z = 3x + 2y
subject to x + 2y < 10, 3x + y < 15, x, y > 0
7. Solve the following Linear Programming Problems graphically : Maximise Z = 5x + 3y
subject to 3x + 5y < 15, 5x + 2y < 10, x > 0, y > 0
1.1.8) Lke[u
8. ykÃku÷ Mkwhu¾ ykÞkusLkLkku «&Lk yk÷u¾Lke heíku Wfu÷ku : z = 5x + 10y Lkwt ykÃku÷ þhíkkuLku yÄeLk {n¥k{ {qÕÞ íkÚkk LÞqLkík{
{qÕÞ {u¤ðku. x ³ 0, y ³ 0, x + y £ 50, 3x + y £ 90
9. Show that the minimum of Z occurs at more than two points : Maximise Z = – x + 2y, subject to the
constraints :
x > 3, x + y > 5, x + 2y > 6, y > 0.
10. Solve the following Linear Programming Problems graphically : Minimise Z = x + 2y
subject to 2x + y > 3, x + 2y > 6, x, y > 0
11. Solve the Linear Programming Problems graphically : Maximise Z = 3x + 4y
subject to the constraints : x + y < 4, x > 0, y > 0
12. Show that the minimum of Z occurs at more than two points : Minimise and Maximise Z = x + 2y
subject to x + 2y ³ 100, 2x – y £ 0, 2x + y £ 200, x, y ³ 0.
, .
CHAPTER 12 STD 12 Date : 16/12/25
Linear Programming Maths
Section [ A ] : 3 Marks Questions
No Ans Chap Sec Que Universal_QueId
1. - Chap 12 [Par... S1 4 QP25P11B1213_P2C12S1Q4
2. - Chap 12 [Par... S2 1 QP25P11B1213_P2C12S2Q1
3. - Chap 12 [Par... S1 2 QP25P11B1213_P2C12S1Q2
4. - Chap 12 [Par... S2 2 QP25P11B1213_P2C12S2Q2
5. - Chap 12 [Par... S2 3 QP25P11B1213_P2C12S2Q3
6. - Chap 12 [Par... S1 5 QP25P11B1213_P2C12S1Q5
7. - Chap 12 [Par... S1 3 QP25P11B1213_P2C12S1Q3
8. - Chap 12 [Par... S7 1.1.8 QP25P11B1213_P2C12S7Q1.1.8
9. - Chap 12 [Par... S1 9 QP25P11B1213_P2C12S1Q9
10. - Chap 12 [Par... S1 6 QP25P11B1213_P2C12S1Q6
11. - Chap 12 [Par... S1 1 QP25P11B1213_P2C12S1Q1
12. - Chap 12 [Par... S1 8 QP25P11B1213_P2C12S1Q8
Welcome To Future - Quantum Paper
