JEE Main & Advanced Mathematics Linear Programming Question Bank

done Self Evaluation Test - Linear Programming Total Questions - 40

• question_answer1)
  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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• question_answer2)
  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 mind-point 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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• question_answer3)
  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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• question_answer4)
  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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• question_answer5)
  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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• question_answer6)
  The feasible region for an LPP is shown shaded in the figure. Let \[Z=3x-4y\] 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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• question_answer7)
  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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• question_answer8)
  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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• question_answer9)
  A shop-keeper 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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• question_answer10)
  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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• question_answer11)
  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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• question_answer12)
  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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• question_answer13)
  Graph of the constrains \[\frac{x}{3}+\frac{y}{4}\le 1,x\ge 0,y\ge 0\] is
  A)
    done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
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• question_answer14)
  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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• question_answer15)
  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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• question_answer16)
  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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• question_answer17)
  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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• question_answer18)
  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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• question_answer19)
  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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• question_answer20)
  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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• question_answer21)
  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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• question_answer22)
  The maximum value of \[z=2x+5y\] subject to the constraints \[2x+5y\le 10,x+2y\ge 1,x-y\le 4,x\ge y\ge 0,\] 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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• question_answer23)
  An oil company required 12000, 20000 and 15000 barrels of high-grade, medium grade and low grade oil, respectively. Refinery A produces 100, 300 and 200 barrels per day of high-grade, medium-grade and low-grade oil, respectively, while refinery B produces 200, 400 and 100 barrels per day of high-grade. Medium-grade 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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• question_answer24)
  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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• question_answer25)
  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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• question_answer26)
  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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• question_answer27)
  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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• question_answer28)
  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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• question_answer29)
                            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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• question_answer30)
  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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• question_answer31)
  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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• question_answer32)
  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 \[Z=40x-20y\] 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 \[Z=40x-20y\] 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 \[Z=40x-20y\] 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 \[Z=40x-20y\] Subject to, \[x\ge 0,y\ge 0\] done clear
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• question_answer33)
  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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• question_answer34)
  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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• question_answer35)
  In equations \[3x-y\ge 3\] and \[4x-y\ge 4\]
  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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• question_answer36)
  \[Z=7x+y,\] 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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• question_answer37)
  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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• question_answer38)
  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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• question_answer39)
  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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• question_answer40)
  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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