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The feasible region for an LPP is always a __________ polygon.

asked Jan 8, 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.

asked Jan 8, 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.

asked Jan 8, 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.

asked Jan 8, 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.

asked Jan 8, 2013 by sreemathi.v

1 answer

In a LPP,the objective function is always ______________.

asked Jan 8, 2013 by sreemathi.v

1 answer

In a LPP,the linear inequalities or restrictions on the variables are called _____________.

asked Jan 8, 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 $(3,0).$

asked Jan 8, 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 =

asked Jan 8, 2013 by sreemathi.v

1 answer

Corner points of the feasible region for an LPP are $(0,2)(3,0),(6,0),(6,8) and (0,5)$.

asked Jan 8, 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: <br>$\begin{array}{1 1}column\; A & column\; B\\maximum\;of \;z &325\end{array}$

asked Jan 8, 2013 by sreemathi.v

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}

asked Jan 8, 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.

asked Jan 8, 2013 by sreemathi.v

1 answer

In order to supplement daily diet,a person wishes to take some X and some wishes Y tablets. 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: \[\] $\begin{matrix} \underline{\text{Tablets} }& \underline{\text{Iron}}&& \underline{\text{Calcium}} && \underline{\text{Vitamin}} \\ \text{X}& 6 &&3 && 2 \\ \text{Y}& 2 &&3 && 4 \\ \end{matrix}$

asked Jan 8, 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.

asked Jan 7, 2013 by sreemathi.v

1 answer

Maximise $Z=x+y$.Subject to $x+4y\leq 8,2x+3y\leq 12,3x+y\leq 9,x\geq 0,y\geq 0$.

asked Jan 7, 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.

asked Jan 7, 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.)?

asked Jan 7, 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.

asked Jan 7, 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?

asked Jan 7, 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.

asked Jan 7, 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.

asked Jan 7, 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.

asked Jan 7, 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.

asked Jan 7, 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.

asked Jan 7, 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.

asked Jan 7, 2013 by sreemathi.v

1 answer

Minimise $Z=13x-15y$ subject to the constraints: $x+y\leq 7,2x-3y+6\geq 0,x\geq 0,y\geq 0$.

asked Jan 7, 2013 by sreemathi.v

1 answer

Maximise the function $Z=11x+7y$,subject to the constraints : $x\leq 3,y\leq 2,x\geq 0,y\geq 0.$

asked Jan 7, 2013 by sreemathi.v

1 answer

Maximise $Z=3x+4y$,subject to the constraints: $x+y\leq 1,x\geq 0,y\geq 0$.

asked Jan 7, 2013 by sreemathi.v

1 answer

Determine the maximum value of $z=11x+7y$ subject to the constraints: $2x+y\leq 6,x\leq 2,y\geq 0.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: If the foot of perpendicular drawn from the origin to a plane is (5,-3,-2), then the equation of plane is $\overrightarrow{r}.(5\hat i-3\hat j-2\hat k)=38.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The equation of aline,which is parallel to $2\hat i\;-\hat j\;+\hat 3k$ and which passes through the point (5,-2,4) is $\Large \frac{x-5}{2}\;=\frac{y-2}{-1}\;=\frac{z-4}{3}.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The vector equation of the line $\Large \frac{x-5}{3}\;=\frac{y+4}{7}\;=\frac{z-6}{2}$ is\[\overrightarrow{r}=(5\hat i-4\hat j+6\hat k)+\lambda(3i\;+7j\;+2k).\]

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The line $\overrightarrow{r}=(2\hat i-3\hat j-\hat k)+\lambda(\hat i-2\hat j-2\hat k)$ lies in the plane $\overrightarrow{r}.(3\hat i-\hat j-\hat k)-2=0$

asked Jan 7, 2013 by sreemathi.v

0 answers

True or False: The angle between the planes $\overrightarrow{r}.(2\hat i-3\hat j+\hat k)=1$ and $\overrightarrow{r}.(\hat i- j)=4$ is $\cos^{-1}\Large \frac{-5}{\sqrt {58}}.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The angle between the line $\overrightarrow{r}=(5\hat i-\hat j-\hat k)+\lambda(2\hat i-\hat j\;+\hat k)$ and the plane $\overrightarrow{r}.(3\hat i-4\hat j-\hat k)-5=0$ is $\sin^{-1}\large \frac{5}{2\sqrt 91}.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The intercepts made by the plane $2x-3y+5z+4=0$ on the co-ordinate axis are $-2,\large\frac{4}{3},\frac{-4}{5}.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The unit vector normal to the plane $x+2y+3z-6=0$ is $\large \frac{1}{\sqrt {14}}\hat i+\frac{2}{\sqrt {14}}\hat j+\frac{3}{\sqrt {14}}\hat k.$

asked Jan 6, 2013 by sreemathi.v

1 answer

The cartesian equation of the plane $\overrightarrow{r}.(\hat i\;+\hat j-\hat k)\;=2$ is ____________.

asked Jan 6, 2013 by sreemathi.v

1 answer

The vector equation of the line through the points $(3,4,-7)$ and $(1,-1,6)$ is ______________.

asked Jan 6, 2013 by sreemathi.v

1 answer

The vector equation of the line $\Large \frac{x-5}{3}\;\frac{y-4}{7}\;\frac{z-6}{2}$ is _______________.

asked Jan 4, 2013 by sreemathi.v

1 answer

The direction cosines of the vector $(2\hat i+2\hat j-\hat k)$ are ___________.

asked Jan 4, 2013 by sreemathi.v

1 answer

A plane passes through the points $(2,0,0) (0,3,0)$ and $(0,0,4)$.The equation of plane is__________.

asked Jan 4, 2013 by sreemathi.v

1 answer

The plane 2x-3y+6z-11=0 makes an angle $\sin^{-1}(\alpha)$ with x-axis.The value of $\alpha$ is equal to

asked Jan 4, 2013 by sreemathi.v

1 answer

The locus represented by $xy+yz=0$ is

asked Jan 4, 2013 by sreemathi.v

1 answer

The area of the quadilateral $ABCD$ where $A(0,4,1),B(2,3,-1),C(4,5,0)$ and $D(2,6,2)$ is equal to

asked Jan 4, 2013 by sreemathi.v

1 answer

The reflection of the point $(\alpha,\beta,\gamma)$ in the xy-plane is

asked Jan 4, 2013 by sreemathi.v

1 answer

The sine of the angle between the straight line $\large \frac{x\;-2}{3}=\frac{y\;-3}{4}=\frac{z\;-4}{5}\;$ and the plane $2x-2y+z=5$ is

asked Jan 4, 2013 by sreemathi.v

1 answer

The distance of the plane $\overrightarrow{r}.\bigg(\frac{2}{7}\hat i+\frac{3}{7}\hat j-\frac{6}{7}\hat k\bigg)$=1 from the origin is

asked Jan 4, 2013 by sreemathi.v

1 answer

If the directions cosines of a line are $k,k,k$ then

asked Jan 4, 2013 by sreemathi.v

1 answer

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