Linear Programming Test

Result

Linear Programming Test - 8

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Weekly Quiz Competition

Question 1

1 / -0

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

47

45

42

43 Solution

Here , maximize Z = 11x + 7y , subject to the constraints :2x + y ≤ 6, x ≤ 2, x ≥ 0, y ≥ 0.

Corner points	Z = 11x +7 y
C(0, 0 )	0
B (2,0)	22
D(2,2 )	36
A(0,6)	42

Hence the maximum value is 42

Question 2
1 / -0

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

A
4

B
6

C
3

D
5

Solution

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

Corner points

Z = 3x +4 y

C(0, 0 )

0

B (1,0)

3

D(0,1 )

4

Hence the maximum value is 4

Question 3

1 / -0

Maximise the function Z = 11x + 7y, subject to the constraints: x ≤ 3, y ≤ 2,x ≥ 0, y ≥ 0.

49

48

47

50 Solution

We have , Maximise the function Z = 11x + 7y, subject to the constraints: x ≤ 3, y ≤ 2,x ≥ 0, y ≥ 0.

Corner points	Z = 11x +7 y
C(0, 0 )	0
B (3,0)	33
D(0,2 )	14
A( 3, 2 )	47

Hence the function has maximum value of 47

Question 4
1 / -0

Minimise Z = 13x – 15y subject to the constraints : x + y ≤ 7, 2x – 3y + 6 ≥ 0 , x ≥ 0, y ≥ 0.

A
– 32

B
– 23

C
– 34

D
– 39

Solution

Here , Minimise Z = 13x – 15y subject to the constraints : x + y ≤ 7, 2x – 3y + 6 ≥ 0 , x ≥ 0, y ≥ 0.

Corner points

Z = 13x - 15 y

C( - 3 , 0 )

-39

B (7,0)

91

D(4,3)

7

Hence the minimum value of the function is -39

Question 5

1 / -0

Maximize Z = 100x + 120y , subject to constraints 2x + 3y ≤ 30, 3x + y ≤ 17, x ≥ 0, y ≥ 0.

1300

1200

1280

1260

Solution

We have , Maximize Z = 100x + 120y , subject to constraints 2x + 3y ≤ 30, 3x + y ≤ 17, x ≥ 0, y ≥ 0.

Corner points	Z = 100x +120 y
P( 0 , 0 )	0
Q(3 , 8)	1260………………….(Max.)
R( 0, 10 )	1200
S(17/3 , 0 )	1700/3

Hence the maximum value is 1260

Question 6

1 / -0

Maximize Z = 5x+3y , subject to constraints x + y ≤ 300 , 2x + y ≤ 360, x ≥ 0, y ≥ 0.

1020

1050

1040

1030

Solution

Here , Maximize Z = 5x+3y , subject to constraints x + y ≤ 300 , 2x + y ≤ 360, x ≥ 0, y ≥ 0.

Corner points	Z = 5x +3 y
P( 0 ,300 )	900
Q(180 , 0)	900
R( 60, 240 )	1020…………………..(Max.)
S(0 , 0 )	0

Hence, the maximum value is 1020

Question 7
1 / -0

Maximize Z = 50x + 60y , subject to constraints x +2 y ≤ 50 , x +y ≥ 30, x, y ≥ 0.

A
1525

B
1600

C
2500

D
1547

Solution

Here , Maximize Z = 50x+60y , subject to constraints x +2 y ≤ 50 , x + y ≥ 30, x, y ≥ 0.

Corner points

Z = 50x +60 y

P( 50 ,0 )

2500

Q(0 , 30)

1800

R( 10, 20 )

1700

Hence, the maximum value is 2500
Question 8
1 / -0

Minimize Z = 50x+60y , subject to constraints x +2 y ≤ 50 , x + y ≥ 30, x, y ≥ 0.

A
1200

B
1700

C
1550

D
1800

Solution

Here , Maximize Z = 50x+60y , subject to constraints x +2 y ≤ 50 , x + y ≥ 30, x, y ≥ 0.

Corner points

Z = 50x +60 y

P( 50 ,0 )

2500

Q(0 , 30).

1800

R( 10, 20 )

1700

Hence the minimum value is 1700

Question 9

1 / -0

Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5).Let F = 4x + 6y be the objective function. The Minimum value of F occurs at

the mid – point of the line segment joining the points (0, 2) and (3, 0) only

(3, 0) only

any point on the line segment joining the points (0, 2) and (3, 0).

(0, 2) only

Solution

Here the objective function is given by : F = 4x +6y .

Corner points	Z = 4x +6 y
(0, 2 )	12........(Min.)
(3,0)	12........(Min.)
(6,0 )	24
(6 , 8 )	72........(Max.)
(0 , 5 )	30

Hence it is clear that the minimum value occurs at any point on the line joining the points (0,2) and (3,0)

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Corner points	Z = 50x +60 y
P( 50 ,0 )	2500
Q(0 , 30)	1800
R( 10, 20 )	1700

Corner points	Z = 13x - 15 y
C( - 3 , 0 )	-39
B (7,0)	91
D(4,3)	7

Linear Programming Test - 8

Result

Linear Programming Test - 8

Score

-

Rank

-

SHARING IS CARING

Question 1

47

45

42

43

Solution

Question 2

4

6

3

5

Solution

Question 3

49

48

47

50

Solution

Question 4

– 32

– 23

– 34

– 39

Solution

Question 5

1300

1200

1280

1260

Solution

Question 6

1020

1050

1040

1030

Solution

Question 7

1525

1600

2500

1547

Solution

Question 8

1200

1700

1550

1800

Solution

Question 9

the mid – point of the line segment joining the points (0, 2) and (3, 0) only

(3, 0) only

any point on the line segment joining the points (0, 2) and (3, 0).

(0, 2) only

Solution

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