Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Linear Programming

Short Answer Type

1. Solve the following Linear Programming Problems graphically:
Maximise Z = 3x + 4y
subject to the constraints: x + y ≤ 4, x ≥ 0, y ≥ 0

324 Views

Long Answer Type

2. Solve the following linear programming problem graphically:
Maximise Z = 4x + y
subject to the constraints: x + y ≤ 50, 3x + y ≤ 90, x ≥ 0, y ≥ 0

335 Views

3. Find the maximum value of f = x + 2 y subject to the constraints:
2x + 3 y ≤ 6
x + 4 y ≤ 4
x, y ≥ 0

151 Views

4. Maximize z = 9 x + 3 y subject to the constraints
2x + 3y ≤ 13
2x + y ≤ 5
x, y ≥ 0

We have to maximize
z = 9x + 3 y
subject to the constraints
2x + 3 y ≤ 13
2x + y ≤ 5
x, y ≥ 0
Consider a set of rectangular cartesian axes OXY in the plane.
It is clear that any point which satisfies x ≥ 0,y ≥ 0 lies in the first quadrant.
Let us draw the graph of 2x + 3y = 13
For x = 0, 3y = 13 $rightwards double arrow space straight y space equals space 13 over 3$

For y = 0, 2x = 13 $rightwards double arrow space straight x space equals space 13 over 2$
$therefore space space space space line space 2 straight x plus 3 straight y space equals space 13 space space meets space OX space in space straight A open parentheses 13 over 2 comma 0 close parentheses space and space OY space in space straight B open parentheses 0 comma space 13 over 3 close parentheses.$
Again we draw the graph of 2x + y = 5
For x = 0, y = 5
For y = 0, 2x = 5 $rightwards double arrow space space straight x space equals space 5 over 2$
$therefore space space space line space 2 straight x plus straight y space equals space 5 space meets space OX space in space straight C open parentheses 5 over 2 comma space 0 close parentheses space and space OY space in space straight D left parenthesis 0 comma space 5 right parenthesis.$

Since feasible region satisfies all the constraints.
$therefore$ OCEB in the feasibe region. The corner points are O(0, 0), $straight C open parentheses 5 over 2 comma space 0 close parentheses comma space straight E left parenthesis 0.5 comma space 4 right parenthesis comma space space straight B open parentheses 0 comma space 13 over 3 close parentheses$
At O(0, 0), z = 9(0) + 3(0) = 0+ 0 = 0
At $straight C open parentheses 5 over 2 comma space 0 close parentheses comma space straight z space equals space 9 space open parentheses 5 over 2 close parentheses space plus space 3 space left parenthesis 0 right parenthesis space equals space 45 over 2 plus 0 space space equals space 45 over 2 space equals space 22.5$
At $straight E thin space left parenthesis 0.5 comma space 4 right parenthesis comma space space straight z space equals space 9 left parenthesis 0.5 right parenthesis space plus space 3 space left parenthesis 4 right parenthesis space equals space 4.5 space plus space 12 space equals space 16.5$
$At space straight B space open parentheses 0 comma space 13 over 3 close parentheses comma space space straight z space equals space 9 space left parenthesis 0 right parenthesis space plus space 3 space open parentheses 13 over 3 close parentheses space equals space 0 plus 13 space equals space 13$
$therefore space space space Maximum space value space of space straight z space is space 22.5 space at space open parentheses 5 over 2 comma 0 close parentheses space space straight i. straight e. comma space space space when space straight x space equals space 5 over 2 comma space space straight y space equals 0$

173 Views

5. Solve the following Linear Programming Problems graphically:
Minimise Z = - 3x + 4 y
subject to the constraints: x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0

149 Views

6. Solve the following Linear Programming Problems graphically:
Minimise Z = 5x + 3y
subject to the constraints: 3x + 5y ≤ 15, 5x + 2y ≤ 10, x ≥ 0, y ≥ 0.

116 Views