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Recent questions and answers in Linear Programming
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Linear Programming
A firm makes two types of furniture : chairs and tables. The contribution to profit for each product as calculated by the accounting department is Rs.20 per chair and Rs.30 per table. Both products are to be processed on three machines $ M_1,M_2 and M_3.$ The time required in hours by each product and total time available in hours per week on each machine are as follows:
cbse
class12
additionalproblem
kvquestionbank2012
ch12
q4
p39
math
answered
Jan 9
by
stefanosstvm
1
answer
If a young man rides his motorcycle at 25 km/hr, he had to spend Rs.2 per km on petrol. If he rides at a faster speed of 40 km/hr, the petrol cost increases at Rs.5 per km. He has Rs.100 to spend on petrol and wishes to find what is the maximum distance he can travel within one hour. Express this as LPP and solve it graphically.
cbse
class12
additionalproblem
kvquestionbank2012
ch12
q6
p39
math
answered
Mar 17, 2015
by
krishvlk
1
answer
A firm has to transport 1200 packages using large vans which can carry 200 packages each and small vans which can take 80 packages each.The cost for engaging each large van is Rs 400 and each small van is Rs 200.Not more than Rs 3000 is to be spent on the job and the number of large vans cannot exceed the number of small vans.What will be the minimum cost?
cbse
class12
ch12
q17
p253
exemplar
sec-c
difficult
math
asked
Feb 1, 2014
by
rvidyagovindarajan_1
1
answer
A merchant plans to sell two types of personal computers, a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant would stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.
cbse
class12
bookproblem
ch12
sec2
q8
p520
sec-c
easy
modelpaper
2012
q29
math
answered
Dec 13, 2013
by
balaji.thirumalai
1
answer
Maximise and minimise Z=3x-4y, subject to $\qquad$ \begin{array}{1 1}x-2y\leq 0\\-3x+y\leq 4\\x-y\leq 6\\x,y\geq 0\end{array}
cbse
class12
ch12
q25
p254
exemplar
sec-c
difficult
math
answered
Sep 3, 2013
by
sreemathi.v
1
answer
A company makes 3 model of calculators:A,B and c at factory I and factory II.The company has orders for at least 6400 calculators of model A;4000 calculator of model B and 4800 calculator of model C.At factory I ,50 calculators of model A,50 of model B and 30 of model C are made every day;at factory II,40 calculators of model A,20 of model B and 40 of model C are made every day.It costs Rs 12000 and Rs 15000 each day to operate factory I and II respectively.Find the number of days each factory should operate to minimize the operating costs and still meet the demand.
cbse
class12
ch12
q24
p254
exemplar
sec-c
difficult
math
answered
Sep 3, 2013
by
sreemathi.v
1
answer
In order to supplement daily diet,a person wishes to take some X and some wishes Y tablets. Y 2 3 4 The person needs atleast 18 milligrams of iron ,21 milligrams of calcium and 16 milligram of vitamins.The price of each tablet of X and Y is Rs.2 and Rs.1 respectively.How many tablets of each should the person take in order to satisfy the above requirement at the minimum cost? The contents of iron ,calcium and vitamins in X and Y(in milligrams per tablet) are given as below: \[\] $\begin{matrix} \underline{\text{Tablets} }& \underline{\text{Iron}}&& \underline{\text{Calcium}} && \underline{\text{Vitamin}} \\ \text{X}& 6 &&3 && 2 \\ \text{Y}& 2 &&3 && 4 \\ \end{matrix}$
cbse
class12
ch12
q23
p254
exemplar
sec-c
difficult
math
answered
Sep 3, 2013
by
sreemathi.v
1
answer
A manufacturer produces two Models of bikes-Model X and Model Y.Model X takes a 6 man-hours to make per unit,while Model Y takes 10 man-hours per unit.There is a total of 450 man-hour available per week.Handling and marketing costs are Rs 2000 and Rs 1000 per unit for models X and Y respectively.The total funds available for these purposes are Rs 80,000 per week.Profits per unit for models X and Y are Rs 1000 and Rs 500,respectively.How many bikes of each model should the manufacturer produce so as to yield a maximum profit.Find the maximum profit.
cbse
class12
ch12
q22
p253
exemplar
sec-c
difficult
math
answered
Aug 30, 2013
by
sreemathi.v
1
answer
A company manufactures two types of sweaters :type A sweaters type B.It costs Rs 360 to make a type A sweater and Rs 120 to make a type B sweater.The company can make at most 300 sweaters and spend at most Rs72,000 a day.The number of sweaters of type B cannot exceed the number of sweaters of type A by more than 100.The company makes a profit of Rs 200 for each sweater of type A and Rs 120 for every sweater of type B.What is the maximum profit (in Rs.)?
cbse
class12
ch12
q19
p253
exemplar
sec-c
difficult
math
answered
Aug 30, 2013
by
sreemathi.v
1
answer
A company manufactures two types of screws A and B.All the screws have to pass through a threading machine and a slotting machine.A box of type A screws requires 2 minutes on the threading machine and 3minutes on the slotting machine.A box of type B screws requires 8 minutes of threading on the threading machine and 2 minutes on the slotting machine.In a week,each machine is available for 60 hours.On selling these screws,the company gets a profit of Rs100 per box on type A screws and Rs170 per box on type B screws.Solve the linear programming problem and determine the maximum profit to the manufacturer.
cbse
class12
ch12
q18
p253
exemplar
sec-c
difficult
math
answered
Aug 30, 2013
by
sreemathi.v
1
answer
A firm has to transport 1200 packages using large vans which can carry 200 packages each and small vans which can take 80 packages each.The cost for engaging each large van is Rs 400 and each small van is Rs 200.Not more than Rs 3000 is to be spent on the job and the number of large vans cannot exceed the number of small vans.What will be the minimum cost?
cbse
class12
ch12
q17
p253
exemplar
sec-c
difficult
math
answered
Aug 30, 2013
by
sreemathi.v
1
answer
A manufacture of electronic circuits has a stock of 200 resistors,120 transistors and 150 capacitors and is required to produce two types of circuits A and B .Type A requires 20 resistors,10 transistors and 10 capacitors .Type B requires 10 resistors,20 transistors and 30 capacitors.If the profit on type A circuit is Rs 50 and that an type B circuit is Rs 60,how many of circuits of type A and type B,should be produced by the manufacturer so as to maximize his profit?Determine the maximum profit.
cbse
class12
ch12
q16
p253
exemplar
sec-c
difficult
math
answered
Aug 30, 2013
by
sreemathi.v
1
answer
A man rides his motorcycle at the speed of 50km/hour.He has to speed Rs 2 per km on petrol.If he rides it at at a faster speed of 80km/hour,the petrol cost increases to Rs 3 per km.He has at most Rs120 to spend on petrol and one hour's time.He wishes to find the maximum distance that he can travel.Express this problem as a linear programming problem.
cbse
class12
ch12
q15
p253
short-answer
exemplar
sec-a
easy
math
answered
Aug 30, 2013
by
sreemathi.v
1
answer
Maximise $Z=x+y$.Subject to $x+4y\leq 8,2x+3y\leq 12,3x+y\leq 9,x\geq 0,y\geq 0$.
cbse
class12
ch12
q21
p253
exemplar
sec-c
medium
math
answered
Aug 29, 2013
by
sreemathi.v
1
answer
A man rides his motorcycle at the speed of 50km/hour.He has to speed Rs 2 per km on petrol.If he rides it at at a faster speed of 80km/hour,the petrol cost increases to Rs 3 per km.He has at most Rs120 to spend on petrol and one hour's time.He wishes to find the maximum distance that he can travel.Determine the maximum distance that the man can travel.
cbse
class12
ch12
q20
p253
exemplar
sec-c
medium
math
answered
Aug 29, 2013
by
sreemathi.v
1
answer
A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?
cbse
class12
bookproblem
ch12
misc
q10
p528
sec-c
difficult
math
answered
Aug 29, 2013
by
sreemathi.v
1
answer
A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table below. \[\] $\begin{matrix} \text{kg per bag:}& \text{Brand P} &\text{Brand Q} \\ \text {Nitrogen} &3 & 3.5\\ \text {Phosphoric Acid}& 1 & 2\\ \text {Potash}&3 &1.5 \\ \text {Chlorine}& 1.5 & 2 \end{matrix}$ \[\] If the grower wants to maximise the amount of nitrogen added to the garden, how many bags of each brand should be added? What is the maximum amount of nitrogen added?
cbse
class12
bookproblem
ch12
misc
q9
p528
sec-c
difficult
math
answered
Aug 29, 2013
by
sreemathi.v
1
answer
A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table below. If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden? \[\] $\begin{matrix} \text{kg per bag:}& \text{Brand P} &\text{Brand Q} \\ \text {Nitrogen} &3 & 3.5\\ \text {Phosphoric Acid}& 1 & 2\\ \text {Potash}&3 &1.5 \\ \text {Chlorine}& 1.5 & 2 \end{matrix}$
cbse
class12
bookproblem
ch12
misc
q8
p527
sec-c
difficult
math
answered
Aug 29, 2013
by
sreemathi.v
1
answer
An oil company has two depots A and B with capacities of 7000 L and 4000 L respectively. The company is to supply oil to three petrol pumps, D, E and F whose requirements are 4500L, 3000L and 3500L respectively. Assuming that the transportation cost of 10 litres of oil is Re 1 per km, how should the delivery be scheduled in order that the transportation cost is minimum? What is the minimum cost? The distances (in km) between the depots and the petrol pumps is given in the following table: \[\] $\begin{matrix} & \underline{\text{Distance in Km}} & \\ \underline{\text{From} \setminus\text{To}}& \text{A}&& \text{B}\\ \text{D}& 7 &&3 \\ \text{E}& 6 &&4 \\ \text{F} & 3 && 2 \end{matrix}$
cbse
class12
bookproblem
ch12
misc
q7
p527
sec-c
difficult
math
answered
Aug 29, 2013
by
sreemathi.v
1
answer
Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively. They supply to 3 ration shops, D, E and F whose requirements are 60, 50 and 40 quintals respectively.
cbse
class12
bookproblem
ch12
misc
q6
p527
sec-c
difficult
math
answered
Aug 28, 2013
by
sreemathi.v
1
answer
An aeroplane can carry a maximum of 200 passengers. A profit of Rs 1000 is made on each executive class ticket and a profit of Rs 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. What is the maximum profit?
cbse
class12
bookproblem
ch12
misc
q5
p526
sec-c
difficult
math
answered
Aug 28, 2013
by
sreemathi.v
1
answer
Determine the maximum value of $z=11x+7y$ subject to the constraints: $2x+y\leq 6,x\leq 2,y\geq 0.$
cbse
class12
ch12
q1
p250
short-answer
exemplar
sec-a
easy
math
answered
Aug 28, 2013
by
sreemathi.v
1
answer
True or False: In a LPP,the maximum value of the objective function $Z=ax+by$ is always finite.
cbse
class12
ch12
q45
p257
true-or-false
exemplar
sec-a
easy
math
answered
Aug 28, 2013
by
sreemathi.v
1
answer
True or False: In a LPP, the minimum value of the objective function $Z=ax+by$ is always 0 if origin is one of the corner point of the feasible region.
cbse
class12
ch12
q44
p257
true-or-false
exemplar
sec-a
easy
math
answered
Aug 28, 2013
by
sreemathi.v
1
answer
True or False: Maximum value of the objective function $Z=ax+by$ in a LPP always occurs at only one corner point of the feasible region.
cbse
class12
ch12
q43
p257
true-or-false
exemplar
sec-a
easy
math
answered
Aug 28, 2013
by
sreemathi.v
1
answer
True or False: If the feasible region for a LPP is unbounded,maximum or minimum of the objective function $Z=ax+by$ may or may not exist
cbse
class12
ch12
q42
p257
true-or-false
exemplar
sec-a
easy
math
answered
Aug 28, 2013
by
sreemathi.v
1
answer
The feasible region for an LPP is always a __________ polygon.
cbse
class12
ch12
q41
p257
fitb
exemplar
sec-a
easy
math
answered
Aug 28, 2013
by
sreemathi.v
1
answer
A corner point of a feasible region is a point in the region which is the _________ of two boundary lines.
cbse
class12
ch12
q40
p257
fitb
exemplar
sec-a
easy
math
answered
Aug 28, 2013
by
sreemathi.v
1
answer
A feasible region of a system of linear inequalities is said to be _________ if it can be enclosed with in a circle.
cbse
class12
ch12
q39
p257
fitb
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
In a LPP if the objective function $Z=ax+by$ has the same maximum value on two corner points of the feasible region,then every point on the line segment joining these two points give the same ________ value.
cbse
class12
ch12
q38
p257
fitb
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
If the feasible region for a LPP is __________,then the optimal value of the objective function $Z=ax+by$ may or may not exist.
cbse
class12
ch12
q37
p257
fitb
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
In a LPP,the objective function is always ______________.
cbse
class12
ch12
q36
p257
fitb
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
In a LPP,the linear inequalities or restrictions on the variables are called _____________.
cbse
class12
ch12
q35
p257
fitb
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
Corner points of the feasible region determined by the system of linear constraints are $(0,3),(1,1)$ and $(3,0).$
cbse
class12
ch12
q34
p256
objective
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
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,Maximum of F - Minimum of F =
cbse
class12
ch12
q33
p256
objective
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
Corner points of the feasible region for an LPP are $(0,2)(3,0),(6,0),(6,8) and (0,5)$.
cbse
class12
ch12
q32
p255
objective
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
The feasible region for an LPP is shown in the figure below ( fig 12.13 in textbook ).Let $F=3x-4y$ be the objective function.Minimum value of $F$ is
cbse
class12
ch12
q31
p255
objective
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
The feasible region for an LPP is shown in the fig.12.13.Let $F=3x-4y$ be the objective function.Maximum value of $F$ is
cbse
class12
ch12
q30
p255
objective
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
The feasible solution for a LPP is shown in fig.12.12.Let $Z=3x-4y$ be the objective function.(Maximum value of $Z$+Minimum value of $Z$) is equal to
cbse
class12
ch12
q29
p255
objective
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
The feasible solution for a LPP is shown in fig.12.12.Let $Z=3x-4y$ be the objective function.Maximum of $Z$ occurs at
cbse
class12
ch12
q28
p255
objective
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
The feasible solution for a LPP is shown in fig.12.12.Let $Z=3x-4y$ be the objective function.Minimum of $Z$ occurs at
cbse
class12
ch12
q27
p255
objective
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
The corner points of the feasible region determined by the system of linear constraints are $(0,0),(0,40),(20,40),(60,20),(60,0)$.The objective function is $Z=4x+3y.$ Compare the quantity in column A and column B: \begin{array}{1 1}column\; A & column\; B\\maximum\;of \;z &325\end{array}
cbse
class12
ch12
q26
p254
objective
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
A company manufactures two types of sweaters :type A sweaters type B.It costs Rs 360 to make a type A sweater and Rs 120 to make a type B sweater.The company can make at most 300 sweaters and spend at most Rs72,000 a day.The number of sweaters of type B cannot exceed the number of sweaters of type A by more than 100.The company makes a profit of Rs 200 for each sweater of type A and Rs 120 for every sweater of type B.Formulate this problem at a LPP to maximise the profit to the company.
cbse
class12
ch12
q14
p253
short-answer
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
A company manufactures two types of screws A and B.All the screws have to pass through a threading machine and a slotting machine.A box of type A screws requires 2 minutes on the threading machine and 3minutes on the slotting machine.A box of type B screws requires 8 minutes of threading on the threading machine and 2 minutes on the slotting machine.In a week,each machine is available for 60 hours.On selling these screws,the company gets a profit of Rs100 per box on type A screws and Rs170 per box on type B screws.
cbse
class12
ch12
q13
p252
short-answer
exemplar
sec-a
easy
math
answered
Aug 27, 2013
by
sreemathi.v
1
answer
A firm has to transport 1200 packages using large vans which can carry 200 packages each and small vans which can take 80 packages each.The cost for engaging each large van is Rs 400 and each small van is Rs 200.Not more than Rs 3000 is to be spent on the job and the number of large vans cannot exceed the number of small vans.Formulate this problem as a LPP given that the objective is to minimize cost.
cbse
class12
ch12
q12
p252
short-answer
exemplar
math
sec-a
answered
Aug 26, 2013
by
sreemathi.v
1
answer
A manufacture of electronic circuits has a stock of 200 resistors,120 transistors and 150 capacitors and is required to produce two types of circuits A and B .Type A requires 20 resistors,10 transistors and 10 capacitors .Type B requires 10 resistors,20 transistors and 30 capacitors.If the profit on type A circuit is Rs 50 and that an type B circuit is Rs 60,formulate this problem as a LPP so that the manufacturer can maximize his profit.
cbse
class12
ch12
q11
p252
short-answer
exemplar
sec-a
easy
math
answered
Aug 21, 2013
by
sreemathi.v
1
answer
In the figure below ,the feasible region (shaded)for a LPP is shown .Determine the maximum and minimum value of $Z=x+2y$
cbse
class12
ch12
q10
p252
short-answer
exemplar
sec-a
easy
math
answered
Aug 20, 2013
by
sreemathi.v
1
answer
The feasible region for a LPP is shown in fig 12.10.Evaluate $Z=4x+y$ at each of the corner points of this region.Find the minimum value of $Z$,if it exists.
cbse
class12
ch12
q9
p251
short-answer
exemplar
sec-a
easy
math
answered
Aug 20, 2013
by
sreemathi.v
1
answer
The feasible region for a LPP is shown in fig.12.9.Find the maximum value of $z=11x+7y$
cbse
class12
ch12
q8
p251
short-answer
exemplar
sec-a
easy
math
answered
Aug 20, 2013
by
sreemathi.v
1
answer
The feasible region for a LPP is shown in fig.12.9.Find the minimum value of $z=11x+7y$
cbse
class12
ch12
q7
p251
short-answer
exemplar
sec-a
easy
math
asked
Aug 20, 2013
by
sreemathi.v
1
answer
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