Recent questions and answers in Linear Programming

Solve the following LPP graphically. Maximize or minimize Z = 3x+5y subject to \[3x-4y\geq-12\]\[2x-y+2\geq0\]\[2x+3y-12\geq0\]\[0\leq x\leq4\]\[y\geq2\]

answered Oct 19, 2020 by rvandana115

1 answer

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:

answered Jan 9, 2017 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.

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?

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.

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}

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.

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. 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: \[\] $\begin{matrix} \underline{\text{Tablets} }& \underline{\text{Iron}}&& \underline{\text{Calcium}} && \underline{\text{Vitamin}} \\ \text{X}& 6 &&3 && 2 \\ \text{Y}& 2 &&3 && 4 \\ \end{matrix}$

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.

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.)?

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.

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?

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.

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.

answered Aug 30, 2013 by sreemathi.v

1 answer

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

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.

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?

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?

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? \[\] $\begin{matrix} \text{kg per bag:}& \text{Brand P} &\text{Brand Q} \\ \text {Nitrogen} &3 & 3.5\\ \text {Phosphoric Acid}& 1 & 2\\ \text {Potash}&3 &1.5 \\ \text {Chlorine}& 1.5 & 2 \end{matrix}$

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: \[\] $\begin{matrix} & \underline{\text{Distance in Km}} & \\ \underline{\text{From} \setminus\text{To}}& \text{A}&& \text{B}\\ \text{D}& 7 &&3 \\ \text{E}& 6 &&4 \\ \text{F} & 3 && 2 \end{matrix}$

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.

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?

answered Aug 28, 2013 by sreemathi.v

1 answer

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

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.

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.

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.

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

answered Aug 28, 2013 by sreemathi.v

1 answer

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

answered Aug 28, 2013 by sreemathi.v

1 answer