Linear Programming Test

Result

Linear Programming Test - 4

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0.25

Let R be the feasible region (convex polygon) for a linear programming problem and let Z = ax + by be the objective function. When Z has an optimal value (maximum or minimum), where the variables x and y are subject to constraints described by linear inequalities,

A
optimal value must occur at a corner point (vertex) of the feasible region.

B
optimal value must occur at the centroid of the feasible region.

C
optimal value must occur at the midpoints of the corner points (vertices) of the feasible region

D
None of these

Solution

Let R be the feasible region (convex polygon) for a linear programming problem and let Z = ax + by be the objective function. When Z has an optimal value (maximum or minimum), where the variables x and y are subject to constraints described by linear inequalities,then , optimal value must occur at a corner point (vertex) of the feasible region.
Question 2
1 / -0.25

Maximise Z = 3x + 4y subject to the constraints: x + y ≤4, x ≥0, y ≥0.

A
Maximum Z = 18 at (1, 4)

B
Maximum Z = 19 at (1, 5)

C
Maximum Z = 16 at (0, 4)

D
Maximum Z = 17 at (0, 5)

Solution

Objective function is Z = 3x + 4 y ……(1).
The given constraints are : x + y ≤4, x ≥0, y ≥0.

therefore Z = 16 is maximum at ( 0 , 4 ) .
Question 3
1 / -0.25

A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines tomanufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximize his profit? Determine the maximum profit.

A
32 packages of screws A and 22 packages of screws B; Maximum profit = Rs 414

B
32 packages of screws A and 20 packages of screws B; Maximum profit = Rs 412

C
30 packages of screws A and 20 packages of screws B; Maximum profit = Rs 410

D
30 packages of screws A and 22 packages of screws B; Maximum profit = Rs 412

Solution

Let number of packages of screws A produced = x
And number of packages of screws B produced = y
Therefore , the above L.P.P. is given as :
Maximise , Z = 7x +10y , subject to the constraints : 4x +6y ≤240 and. 6x +3y ≤240 i.e. 2x +3y ≤120 and 2x +y ≤80 , x, y ≥0.

i.e 30 packages of screws A and 20 packages of screws B; Maximum profit = Rs 410.
Question 4
1 / -0.25

Determine the maximum value of Z = 11x + 7y subject to the constraints :2x + y ≤6, x ≤2, x ≥0, y ≥0.

A
47

B
45

C
42

D
43

Solution

Here , maximize Z = 11x + 7y , subject to the constraints :2x + y ≤6, x ≤2, x ≥0, y ≥0.
Question 5
1 / -0.25

The feasible region for a LPP is shown in Figure. Find the minimum value of Z = 11x + 7y.

A
22

B
20

C
19

D
21

Solution
Question 6
1 / -0.25

Let R be the feasible region for a linear programming problem, and let Z = ax + by be the objective function. If R is bounded, then

A
the objective function Z has only a maximum value on R

B
the objective function Z has only a minimum value on R

C
the objective function Z has both a maximum and a minimum value on R

D
the objective function Z has no minimum value on R

Solution

Let R be the feasible region for a linear programming problem, and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R .
Question 7
1 / -0.25

Minimise Z = –3x + 4 y subject to x + 2y ≤8, 3x + 2y ≤12, x ≥0, y ≥0.

A
Minimum Z = –14 at (5, 0)

B
Minimum Z = –12 at (4, 0)

C
Minimum Z = –15 at (5, 1)

D
Minimum Z = –13 at (4, 1)

Solution

Objective function is Z = - 3x + 4 y ……………………(1).
The given constraints are : x + 2y ≤8, 3x + 2y ≤12, x ≥0, y ≥0.

Here , Z = -12 is minimum at C (4 , 0) .
Question 8
1 / -0.25

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximize his profit?

A
5 Pedestal lamps and 4 wooden shades; Maximum profit = Rs 35

B
5 Pedestal lamps and 5 wooden shades; Maximum profit = Rs 38

C
4 Pedestal lamps and 4 wooden shades; Maximum profit = Rs 32

D
4 Pedestal lamps and 5 wooden shades; Maximum profit = Rs 36

Solution

Let number of pedestal lamps manufactured = x
And number of wooden shades manufactured = y
Therefore , the above L.P.P. is given as :
Maximise , Z = 5x +3y , subject to the constraints : 2x +y ≤12 and. 3x +2y ≤20 , x, y ≥0.

Here Z = 32 is maximum.
i.e 30 packages of screws A and 20 packages of screws B; Maximum profit = Rs 410.
i.e. 4 Pedestal lamps and 4 wooden shades; Maximum profit = Rs 32 .
Question 9
1 / -0.25

Maximize Z = 3x + 4y, subject to the constraints: x + y ≤1, x ≥0, y ≥0.

A
2

B
4

C
6

D
5

Solution

Here , maximize , Z = 3x + 4y, subject to the constraints: x + y ≤1, x ≥0, y ≥0.
Question 10
1 / -0.25

The feasible region for a LPP is shown in Figure. Find the maximum value of Z = 11x + 7y.

A
49

B
50

C
48

D
47

Solution