LINEAR PROGRAMMING
1. Maximize Z = 5x + 3y subject to constraints 3x + 5y ≤ 15, 5x + 2y ≤ 10 and x ≥ 0, y
≥0.
2. Determine graphically the minimum value of the objective function Z = -50x +
20y subject to 2x – y ≥ - 5, 3x + y ≥ 3, 2x – y ≤12 and x≥ 0, y ≥0.
3. Maximize Z = 2x + 5y subject to constraints x + y ≤ 4 , 3x + 3y≥ 18 and x ≥ 0, y≥0.
4. Maximize Z = 5x + 3y subject to constraints x + y ≥ 2, x + 2y ≥ 3 and x ≥ 0, y≥0.
5. Maximize Z = 16x + 20y subject to constraints x + 2y ≥ 10, x + y ≤ 6, 3x + y ≥ 8 and
x ≥ 0, y≥0.
6. Determine graphically the maximum value of the objective function Z = 8x + 9y
subject to 3x - 2y ≤ 6, 2x + 3y ≤ 6 and x≥ 0, y ≥0.
7. The common region determined by all the constraints of a linear programming
problem is :
A) An unbounded region B) an optimal region
C) a bounded region D) a feasible region
8. If A1 denotes the area of the region bounded y2 = 4x, x = 1 and x-axis in the first
quadrant and A2 denotes the area of region bounded by y2 = 4x, x = 4, find A1 : A2.
9. The month of September is celebrated as the Rashtriya Poshan Maah across the
country. Following a healthy and balanced diet is crucial in order to supply the
body with the proper nutrients it needs. A balanced diet also keeps us mentally
fit and promotes improved level of energy.
A dietician wishes to minimize the cost of a diet involving two types of food X(x
kg) and food Y(y kg) which are available at the rate of Rs. 16/kg and Rs. 20/kg
respectively. The feasible region satisfying the constraints is shown in figure.
On the basis of the above information, answer the following questions :
i) Identify and write all the constraints which determine the given feasible
region in figure.
ii) If the objective is to minimize cost Z = 16x + 20y, find the values of x and y
at which cost is minimum. Also, find minimum cost assuming that
minimum cost is possible for the given unbounded region.
10. Solve the following LPP graphically:
Minimise Z = 60 x + 80 y; subject to constraints 3x + 4y ≥8, 5x + 2y ≥ 11 and x, y
≥ 0.
11. Which of the following satisfies both the inequations 2x + y ≤ 10 and x + 2y ≥ 8?
A) (-2, 4) B) (3, 2) C) (-5, 6) D) (4, 2)
12. The solution set of the inequation 3x + 5y < 7 is :
A) Whole xy-plane except the points lying on the line 3x + 5y = 7
B) Whole xy-plane along with the points lying on the line 3x + 5y = 7
C) Open half plane containing the origin except the points lying on the line 3x +
5y = 7.
D) Open half plane not containing the origin.
13. Solve the following LPP graphically:
Maximise Z = −¿3x −¿ 5y; subject to constraints −2x + y ≤ 4, x + y ≥ 3, x – 2y ≤ 2
and x, y≥ 0.
14. Solve the following LPP graphically:
Maximise Z = 70 x +¿ 40y; subject to constraints 3x + 2y ≤ 9, 3x + y ≤ 9 and x, y≥ 0.
15. The number of feasible solutions of LPP given as Maximize Z = 15x + 30y subject
to constraints: 3x + y ≤ 12, x + 2y ≤ 10 and x, y≥ 0 is
A) 1 B) 2 C) 3 D) Infinite
16. The feasible region of a LPP is shown in the figure below:
A) x + 2y ≥ 4, x + y ≤ 3, x≥ 0, y ≥ 0
B) x + 2y ≤ 4, x + y ≤ 3, x≥ 0, y ≥ 0
C) x + 2y ≥ 4, x + y ≥ 3, x≥ 0, y ≥ 0
D) x + 2y ≥ 4, x + y ≤ 3, x≤ 0, y ≤ 0
E) Solve the following LPP graphically:
17. Maximise Z = x +¿ 2y; subject to constraints 2x + y ≥ 3, x + 2y ≥ 6 and x, y≥ 0.
