
The Solution set of constraints \[x+2y\ge 11,\]\[3x+4y\le 30,\]\[2x+5y\le 30\] and \[x\ge 0,\]\[y\ge 0,\] includes the point
A)
(2, 3) done
clear
B)
(3, 2) done
clear
C)
(3, 4) done
clear
D)
(4, 3) done
clear
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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
A)
\[(0,2)\] Only done
clear
B)
\[(3,0)\] Only done
clear
C)
The mindpoint of the line segment joining the points \[(0,2)\] and \[(3,\,\,2)\]only done
clear
D)
Any point on the line segment joining the points \[(0,2)\] and \[(3,0)\] done
clear
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The solution set of the following system of in equations: \[x+2y\le 3,\] \[3x+4y\ge 12,\]\[x\ge 0,\]\[y\ge 1,\] is
A)
Bounded region done
clear
B)
Unbounded region done
clear
C)
Only one point done
clear
D)
Empty set done
clear
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Every gram of wheat provides 0.1 g of proteins and 0.25g of carbohydrates. The corresponding values of rice are 0.05 g and 0.5 g respectively. Wheat costs Rs. 4 per kg and rice Rs. 6. The minimum daily requirements of proteins and carbohydrates for an average child are 50 g and 200 g respectively. Then in what quantities should wheat and rice be mixed in the daily diet to provide minimum daily requirement of proteins and carbohydrates at minimum cost
A)
400, 200 done
clear
B)
300, 400 done
clear
C)
200, 400 done
clear
D)
400, 300 done
clear
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The solution of linear programming problem maximize \[z=3{{x}_{1}}+5{{x}_{2}}\] Subject to \[3{{x}_{1}}+2{{x}_{2}}\le 18,\]\[{{x}_{1}}\le 4,{{x}_{2}}\le 6,{{x}_{1}}\ge 0,{{x}_{2}}\ge 0\] is
A)
\[{{x}_{1}}=2,{{x}_{2}}=0,z=6\] done
clear
B)
\[{{x}_{1}}=2,{{x}_{2}}=6,z=36\] done
clear
C)
\[{{x}_{1}}=4,{{x}_{2}}=3,z=27\] done
clear
D)
\[{{x}_{1}}=4,{{x}_{2}}=6,z=42\] done
clear
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The feasible region for an LPP is shown shaded in the figure. Let \[Z=3x4y\] be the objective function. Minimum of Z occurs at
A)
(0, 0) done
clear
B)
(0, 8) done
clear
C)
(5, 0) done
clear
D)
(4, 10) done
clear
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The maximum value of \[z=3x+4y\] subject to the condition \[x+y\le 40,x+2y\le 60,x,y\ge 0\] is
A)
130 done
clear
B)
120 done
clear
C)
40 done
clear
D)
140 done
clear
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Consider \[\frac{x}{2}+\frac{y}{4}\ge 1\] and \[\frac{x}{3}+\frac{y}{2}\le 1,x,y\ge 0.\] Then number of possible solutions are:
A)
Zero done
clear
B)
Unique done
clear
C)
Infinite done
clear
D)
None of these done
clear
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A shopkeeper deals in the sale of TV s and VCPs. He has 5.2 lacs to invest. He has only space for 50 pieces. ATV costs 20,000/ and a VCP costs 8,000/ From a TV and VCP he earns a profit of 1500/ and 800/ respectively. Assuming that he sells all the items that he purchases, the number of TVs and VCPs he should buy in order to Maximize his profit, is equal to
A)
60, 000 done
clear
B)
55, 000 done
clear
C)
51, 000 done
clear
D)
47, 000 done
clear
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The maximum value of \[z=4x+3y\] subject to the constraints \[3x+2y\ge 160,5x+2y\ge 200,x+2y\ge 80,\]\[x,y\ge 0\] is.
A)
320 done
clear
B)
300 done
clear
C)
230 done
clear
D)
None done
clear
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The constraints\[{{x}_{1}}+{{x}_{2}}\le 1,{{x}_{1}}+3{{x}_{2}}\le 9,{{x}_{1}},{{x}_{2}}\ge 0\] Define on
A)
Bounded feasible space done
clear
B)
Unbounded feasible space done
clear
C)
Both bounded and unbounded feasible space done
clear
D)
None of these done
clear
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A company manufactures two types of products A and B. The storage capacity of its go down is 100 units. Total investment amount is 30,000. The cost price of A and B are 400 and 900 respectively. Suppose all the product have sold and per unit profit is 100 and 120 through A and B respectively. If X units of A and Y units of B be produced, then two linear constraints and is profit line are respectively
A)
\[x+y=100;4x+9y=300,100x+120y=c\] done
clear
B)
\[x+y\le 100;4x+9y\le 300,x+2y=c\] done
clear
C)
\[x+y\le 100;4x+9y\le 300,100x+120y=c\] done
clear
D)
\[x+y\le 100;9x+4y\le 300,x+2y=c\] done
clear
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Graph of the constrains \[\frac{x}{3}+\frac{y}{4}\le 1,x\ge 0,y\ge 0\] is
A)
B)
C)
D)
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Consider the objective function \[Z=40x+50y.\] The minimum number of constraints that are required to maximize Z are
A)
4 done
clear
B)
2 done
clear
C)
3 done
clear
D)
1 done
clear
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Maximize \[Z=3x+5y,\] subject to \[x+4y\le 24,\]\[3x+y\le 21,\]\[x+y,\le 9,\]\[x\ge 0,y\ge 0,\] is
A)
\[20\,at\,(1,0)\] done
clear
B)
\[30\,\,at\,\,(0,6)\] done
clear
C)
\[37\,at\,(4,5)\] done
clear
D)
\[33\,\,at\,\,(6,3)\] done
clear
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The maximum value of \[z=4x+2y\]subject to constraints \[2x+3y\le 18,x+y\ge 10\] and \[x,y\ge 0\], is
A)
36 done
clear
B)
40 done
clear
C)
20 done
clear
D)
None of these done
clear
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Feasible region for an LPP is shown shaded in the following figure. Minimum of \[Z=4x+3y\]occurs at the point.
A)
(0, 8) done
clear
B)
(2, 5) done
clear
C)
(4, 3) done
clear
D)
(9, 0) done
clear
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A wholesale merchant wants to start the business of cereal with 24000. Wheat is 4000 per quintal and rice is 600 per quintal. He has capacity to store 200 quintal cereal. He earns the profit 25 per quintal on wheat and 40 per quintal on rice. If he store x quintal rice and y quintal wheat then for maximum profit, the objective function is
A)
\[25x+40y\] done
clear
B)
\[40x+25y\] done
clear
C)
\[400x+600y\] done
clear
D)
\[\frac{400}{40}x+\frac{600}{25}y\] done
clear
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Which of the following is not a vertex of the positive region bounded by the inequalities \[2x+3y\le 6,5x+3y\le 15\] and \[x,y\ge 0\]
A)
(0, 2) done
clear
B)
(0, 0) done
clear
C)
(3, 0) done
clear
D)
All of these done
clear
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The maximum value \[z=5x+2y,\]subject to the constraints \[x+y\le 7,x+2y\le 10,x,y\ge 0\]is
A)
10 done
clear
B)
26 done
clear
C)
35 done
clear
D)
70 done
clear
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For the constraint of a linear optimizing function\[z={{x}_{1}}+{{x}_{2}},\] Given by \[{{x}_{1}}+{{x}_{2}}\le 1,3{{x}_{1}}+{{x}_{2}}\ge 3\]and\[{{x}_{1}},{{x}_{2}}\ge 0\].
A)
There are two feasible regions done
clear
B)
There are infinite feasible regions done
clear
C)
There is no feasible region done
clear
D)
None of these done
clear
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The maximum value of \[z=2x+5y\] subject to the constraints \[2x+5y\le 10,x+2y\ge 1,xy\le 4,x\ge y\ge 0,\] Occurs at
A)
Exactly one pint done
clear
B)
Exactly two points done
clear
C)
Infinitely many points done
clear
D)
None of these done
clear
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An oil company required 12000, 20000 and 15000 barrels of highgrade, medium grade and low grade oil, respectively. Refinery A produces 100, 300 and 200 barrels per day of highgrade, mediumgrade and lowgrade oil, respectively, while refinery B produces 200, 400 and 100 barrels per day of highgrade. Mediumgrade and low grade oil, respectively. If refinery A costs 400 per day and refinery B costs 300 per day to operate, then the days should each he run to minimize costs while satisfying requirements are
A)
30, 60 done
clear
B)
60, 30 done
clear
C)
40, 60 done
clear
D)
60, 40 done
clear
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A vertex of bounded region of inequalities \[x\ge 0\]\[x+2y\ge 0\] and \[2x+y\le 4\]is
A)
(1, 1) done
clear
B)
(0, 1) done
clear
C)
(3, 0) done
clear
D)
(0, 4) done
clear
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Which of these terms is not used in a linear programming problem?
A)
Slack variables done
clear
B)
Objective function done
clear
C)
Concave region done
clear
D)
Feasible solution done
clear
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The maximum value of \[z=6x+8y\] subject to constraints \[2x+y\le 30,x+2y\le 24\] and \[x\ge 0,y\ge 0\] is
A)
90 done
clear
B)
120 done
clear
C)
96 done
clear
D)
240 done
clear
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Consider: \[z=3x+2y\] Minimize subject to:\[x+y\ge 8\]\[3x+5y\le 15\]\[x,y\ge 0\] It has:
A)
Infinite feasible solutions done
clear
B)
Unique feasible solution done
clear
C)
No feasible solution done
clear
D)
None of these done
clear
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The number of corner points of the L.P.P. Max \[Z=20x+3y\] subject to the constraints \[x+y\le 5,2x+3y\le 12,x\ge 0,y\ge 0\] are
A)
4 done
clear
B)
3 done
clear
C)
2 done
clear
D)
1 done
clear
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The maximum value of \[z=3x+2y,\]subjected to the conditions \[x+2y\ge 2,x+2y\le 8,x,y\ge 0\] is
A)
32 done
clear
B)
24 done
clear
C)
40 done
clear
D)
None of these done
clear
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The Maximum value of \[z=5x+3y\], subjected to the conditions\[3x+5y\le 15,5x+2y\le 10,x,y\ge 0\]is
A)
\[\frac{235}{19}\] done
clear
B)
\[\frac{325}{19}\] done
clear
C)
\[\frac{523}{19}\] done
clear
D)
\[\frac{532}{19}\] done
clear
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The constraints \[{{x}_{1}}+{{x}_{2}}\le 1,{{x}_{1}}+3{{x}_{2}}\le 9;\]\[{{x}_{1}},{{x}_{2}}\ge 0\] defines on
A)
Bounded feasible space done
clear
B)
Unbounded feasible space done
clear
C)
Both bounded and unbounded feasible space done
clear
D)
None of these done
clear
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A brick manufacture has two depots A and B, with stocks of 30000 and 20000 bricks respectively. He receive orders form three builders P, Q and R for 15000, 20,000 and 15000 bricks respectively. The cost (in) of transporting 1000 bricks to the builders form the deposits as given in the table.
To From  Transportation cost per 1000 bricks (in Rs.) 
P  Q  R 
A  40  20  20 
B  20  60  40 
The manufacturer wished to find how to fulfill the order so that transportation cost is minimum. Formulation of the L.P.P., is given as
A)
Minimize \[Z=40x20y\] Subject to, \[x+y\ge 15,x+y\le 30,x\ge 15,y\le 20,\]\[x\ge 0,y\ge 0\] done
clear
B)
Minimize \[Z=40x20y\] Subject to, \[x+y\ge 15,x+y\le 30,x\le 15,y\ge 20,\]\[x\ge 0,y\ge 0\] done
clear
C)
Minimize \[Z=40x20y\] Subject to, \[x+y\ge 15,x+y\le 30,x\le 15,y\le 20,\]\[x\ge 0,y\ge 0\] done
clear
D)
Minimize \[Z=40x20y\] Subject to, \[x\ge 0,y\ge 0\] done
clear
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The inequalities \[5x+4y\ge 20,x\le 6,y\le 4\]from
A)
A square done
clear
B)
A rhombus done
clear
C)
A triangle done
clear
D)
A quadrilateral done
clear
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Maximize \[Z=4x+6y,\] subject to \[3x+2y\le 12,\]\[x+y\ge 4,x,y\ge 0,\]is
A)
\[16\,\,at\,(4,0)\] done
clear
B)
\[24\,\,at\,\,(0,4)\] done
clear
C)
\[24\,\,at\,(6,0)\] done
clear
D)
\[36\,\,at\,(0,6)\] done
clear
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In equations \[3xy\ge 3\] and \[4xy\ge 4\]
A)
Have solution for positive x and y done
clear
B)
Have no solution for positive x and y done
clear
C)
Have solution for all x done
clear
D)
Have solution for all y done
clear
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\[Z=7x+y,\] subject to\[5x+y\ge 5,x+y\ge 3,x\ge 0,y\ge 0.\] The minimum value of Z occurs at
A)
(3, 0) done
clear
B)
\[\left( \frac{1}{2},\frac{5}{2} \right)\] done
clear
C)
(7, 0) done
clear
D)
(0, 5) done
clear
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The true statement for the graph of in equations\[3x+2y\le 6\] and \[6x+4y\ge 20,\] is
A)
Both graph are disjoint done
clear
B)
Both contain (0, 3) done
clear
C)
Both contain point (1, 1) done
clear
D)
None of these done
clear
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Shamli wants to invest 50,000 in saving certificates and PPF. She wants to invest at least 15,000 in saving certificate and at least 20, 000 in PPF. The rate of interest on saving certificates is \[8%P.a.\]and that on PPF is 9% P. a formulation of the above problem as LPP to determine maximum Yearly income, is
A)
Maximize \[Z=0.08x+0.09y\] subject to, \[x+y\le 50,000,x\ge 15000,\] done
clear
B)
Maximize \[Z=0.08x+0.09y\] subject o, \[x+y\le 50,000,x\ge 15000,y\le 20,000\] done
clear
C)
Maximize \[Z=0.08x+0.09y\]subject to, \[x+y\le 50,000,x\le 15000,y\ge 20,000\] done
clear
D)
Maximize \[Z=0.08x+0.09y\] subject to, \[x+y\le 50,000,x\le 15000,y\le 20,000\] done
clear
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The maximum value of \[P=x+3y\] such that \[2x+y\le 20,x+2y\le 20,x\ge 0,y\ge 0\] is
A)
10 done
clear
B)
60 done
clear
C)
30 done
clear
D)
None of these done
clear
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A printing company prints two types of magazines A and B. The company earns 10 and 15 on each magazine A and B respectively. These are processed on three machines I, II & III and total time in hours available per week on each machine is as follows:
Magazine \[\to \]  A(x)  B(y)  Time available 
\[\downarrow \]Machine    
I  2  3  36 
II  5  2  50 
III  2  6  60 
The number of constraints is
A)
3 done
clear
B)
4 done
clear
C)
5 done
clear
D)
6 done
clear
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