HARD
12th West Bengal Board
IMPORTANT
Earn 100

Find all the optimal solution of the LPP in which the objective function z=-16x-4y is to be minimized subject to the constraints 4x+y36, 2x7y+420, 4x+3y12 where x0, y0. Determine also the minimum value of z.

Important Questions on Linear Programming Problems

HARD
12th West Bengal Board
IMPORTANT
Determine the maximum and minimum values (if exists) of the objective function z=9x-4y subject to the constraints 3x2y6, 3xy9, x7y7 where x0, y0.
HARD
12th West Bengal Board
IMPORTANT
Find out the corner point P in the feasible region of the LPP in which the objective function z=-2x+6y is maximum subject to the constraints 3x+5y15, xy+30, x3y+150, where x0, y0. Determine also the maximum value of z. Does there exist the minimum value of z with respect to same set of constraints? Answer with proper reason.
HARD
12th West Bengal Board
IMPORTANT
The constraints of an LPP with two decision variables x, y are given to be y3x, 3x+4y15 and 2x+y10 where x0, y0. The objective functions z of this LPP is maximum at the point 3.5, 3. Determine z if max z=30.
MEDIUM
12th West Bengal Board
IMPORTANT

Maximize Z=3x+5y

Subject to

x+2y20

x+y15

y5

x,y0

HARD
12th West Bengal Board
IMPORTANT

Maximize z=x+y

subject to x+2y10

x+y1

y4

where, x, y0.

HARD
12th West Bengal Board
IMPORTANT

Minimize z=3x+2y

subject to 2x+y14

2x+3y22

x+y5

where x, y0.

MEDIUM
12th West Bengal Board
IMPORTANT

A manufacturer has installed three machines to produce two items A and B (say). Machine M1 and M2 are capable of being operated for at most 10 hours and 12 hours per day. Machine M3 must operate for at least 6 hours a day. To produce a unit of item A, the manufacturer has to operate M1, M2, M3 for 2 hours, 1 hour and 2 hours respectively. Machines M1, M2 and M3 are to be used for 1 hour, 3 hours and 2 hours respectively to produce one unit of item B. The manufacturer makes a profit of Rs. 8 on each unit of A and a profit of Rs. 6 on each unit of item B. It is assumed that he can sell out all the items he can produce. Formulate this problem as an LPP in which profit is made maximum.

EASY
12th West Bengal Board
IMPORTANT

A factory is engaged in manufacturing two products A and B which involves lathe work, grinding and assembling. The cutting, grinding and assembling times required for one unit on A are 2, 1 and 1 hours respectively. Similarly 3, 1 and 3 hours for one unit of B. The profit on A and B are Rs.2, Rs.3 per unit respectively. Assuming that there are available 300 hours of lathe time, 200 hours of grinding time and 240 hours of assembling time, the manufacturer wants to produce different type of items A, B, C in such a way that the profit turns out to be maximum. Formulate the above as an LPP.