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Linear Programming

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Q 1. Shaded region is represented by

{tex} 4 x - 2 y \leq 3 {/tex}

{tex} 4 x - 2 y \leq - 3 {/tex}

{tex} 4 x - 2 y \geq 3 {/tex}

{tex} 4 x - 2 y \geq - 3 {/tex}

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Q 2. For the constraint of a linear optimizing function {tex} z = x _ { 1 } + x _ { 2 } , {/tex} given by {tex} x _ { 1 } + x _ { 2 } \leq 1,3 x _ { 1 } + x _ { 2 } \geq 3 {/tex} and {tex} x _ { 1 } , x _ { 2 } \geq 0 {/tex}

There are two feasible regions

There are infinite feasible regions

There is no feasible region

None of these

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Q 3. The intermediate solutions of constraints must be checked by substituting them back into

Objective function

Constraint equations

Not required

None of these

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Q 4. A basic solution is called non-degenerate, if

All the basic variables are zero

None of the basic variables is zero

At least one of the basic variables is zero

None of these

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Q 5. The feasible solution of a L.P.P. belongs to

First and second quadrant

First and third quadrant

Second quadrant

Only first quadrant

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Q 6. The true statement for the graph of inequations {tex} 3 x + 2 y \leq 6 {/tex} and {tex} 6 x + 4 y \geq 20 {/tex}, is

Both graphs are disjoint

Both do not contain origin

Both contain point {tex} ( 1,1 ) {/tex}

None of these

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Q 7. The value of objective function is maximum under linear constraints

At the centre of feasible region

At {tex} ( 0,0 ) {/tex}

At any vertex of feasible region

The vertex which is at maximum distance from {tex} ( 0,0 ) {/tex}

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Q 8. The region represented by {tex} 2 x + 3 y - 5 \leq 0 {/tex} and {tex} 4 x - 3 y + 2 \leq 0 {/tex}, is

Not in first quadrant

Bounded in first quadrant

Unbounded in first quadrant

None of these

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Q 9. Objective function of a L.P.P, is

A constraint

A function to be optimized

A relation between the variables

None of these

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Q 10. Shaded region is represented by

{tex} 2 x + 5 y \geq 80 ,\ x + y \leq 20 ,\ x \geq 0 ,\ y \leq 0 {/tex}

{tex} 2 x + 5 y \geq 80 ,\ x + y \geq 20 ,\ x \geq 0 ,\ y \geq 0 {/tex}

{tex} 2 x + 5 y \leq 80 ,\ x + y \leq 20 ,\ x \geq 0 ,\ y \geq 0 {/tex}

{tex} 2 x + 5 y \leq 80 ,\ x + y \leq 20 ,\ x \leq 0 ,\ y \leq 0 {/tex}

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Q 11. The graph of inequations {tex} x \leq y {/tex} and {tex} y \leq x + 3 {/tex} is located in

II quadrant

I, II quadrants

I, II, III quadrants

II, III, IV quadrants

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Q 12. Mohan wants to invest the total amount of Rs.15,000 in saving certificates and national saving bonds. According to rules, he has to invest at least Rs. 2000 in saving certificates and Rs. 2500 in national saving bonds. The interest rate is 8{tex}\% {/tex} on saving certificate and 10{tex} \% {/tex} on national saving bonds per annum. He invest Rs. {tex} x {/tex} in saving certificates and Rs. {tex} y{/tex} in national saving bonds. Then the objective function for this problem is

{tex} 0.08 x + 0.10 y {/tex}

{tex} \frac { x } { 2000 } + \frac { y } { 2500 } {/tex}

{tex} 2000 x + 2500 y {/tex}

{tex} \frac { x } { 8 } + \frac { y } { 10 } {/tex}

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Q 13. The minimum value of {tex} z = 2 x _ { 1 } + 3 x _ { 2 } {/tex} subject to the constraints {tex} 2 x _ { 1 } + 7 x _ { 2 } \geq 22 ,\ x _ { 1 } + x _ { 2 } \geq 6,\ 5 x _ { 1 } + x _ { 2 } \geq 10 {/tex} and {tex} x _ { 1 } ,\ x _ { 2 } \geq 0 {/tex} is

14

20

10

16

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