Recent questions tagged ch12

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:

asked Feb 5, 2013 by meena.p

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An oil company has tow depots A and B with capacities of 7000L and 4000L respectively. The company is to supply oil to three petrol pumps D, E and F whose requirements are 4500L, 3000L and 3500L respectively. The distances (in km) between the depots and the petrol pumps is given in the following table:

asked Feb 5, 2013 by meena.p

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A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A, while each packet of the same quality of food Q contains 3 units of calcium, 20 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and almost 300 units of cholesterol. How many packets of each food should be used to maximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A?

asked Feb 5, 2013 by meena.p

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A toy company manufactures two types of doll; a basic version-doll A and a deluxe version doll B. Each doll of type B takes twice as long as to produce as one of type A, and the company would have time to make a maximum of 2000 per day if it produces only the basic version. The supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which there are only 600 per day available. If company makes profit of Rs.3 and Rs.5 per doll, respectively, on doll A and B; how many each should be produced per day in order to maximize profit.

asked Feb 5, 2013 by meena.p

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True or False: In a LPP,the maximum value of the objective function $Z=ax+by$ is always finite.

asked Jan 8, 2013 by sreemathi.v

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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.

asked Jan 8, 2013 by sreemathi.v

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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.

asked Jan 8, 2013 by sreemathi.v

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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

asked Jan 8, 2013 by sreemathi.v

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

asked Jan 8, 2013 by sreemathi.v

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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

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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

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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

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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

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In a LPP,the objective function is always ______________.

asked Jan 8, 2013 by sreemathi.v

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

asked Jan 8, 2013 by sreemathi.v

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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

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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,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

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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

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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

Solve the following Linear Programming Problems graphically: Maximise $Z = 3x + 4y$ . subject to the constraints : $x + y \leq 4, x \geq 0, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Solve the following Linear Programming Problems graphically: Minimise $Z =$ –$3x + 4 y$ subject to $ x + 2y \leq 8, 3x + 2y \leq 12, x \geq 0, y\geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Solve the following Linear Programming Problems graphically: Maximise $Z = 5x + 3y$ subject to $3x + 5y \leq 15, 5x + 2y \leq 10, x \geq 0, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Solve the following Linear Programming Problems graphically: Minimise $Z = 3x + 5y$. such that $ x + 3y \geq 3, x + y \geq 2, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Solve the following Linear Programming Problems graphically: Maximise $Z = 3x + 2y$ subject to $x + 2y \leq 10, 3x + y \leq 15, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Solve the following Linear Programming Problems graphically: Minimise $Z = x + 2y$, subject to $2x + y \geq 3, x + 2y \geq 6, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Show that the minimum of $Z$ occurs at more than two points. Minimise and Maximise $Z = 5x + 10 y$ subject to $x + 2y \leq 120, x + y \geq 60, x – 2y \geq 0, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Show that the minimum of Z occurs at more than two points. Minimise and Maximise $Z = x + 2y$ subject to $ x + 2y \geq 100, 2x – y \leq 0, 2x + y \leq 200; x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Show that the minimum of Z occurs at more than two points. Maximise $z = – x + 2y$, subject to the constraints: $ x \geq 3, x + y \geq 5, x + 2y \geq 6, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Show that the minimum of Z occurs at more than two points. Maximise $Z = x + y$, subject to$\; x $– $y\leq –1, -x + y \leq 0, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

The corner points of the feasible region determined by the following system of linear inequalities: 2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). Let Z = px + qy, where p, q > 0. The condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is (A) p = q (B) p = 2q (C) p = 3q (D) q = 3p?

asked Nov 16, 2012 by fingeazy

1 answer

There are two types of fertilisers $F_{1} $ and $F_{2} $. $F_{1} $ consists of 10% nitrogen and 6% phosphoric acid and $F_{2} $ consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If $F_{1} $ costs Rs 6/kg and $F_{2} $ costs Rs 5/kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?

asked Nov 16, 2012 by fingeazy

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