Manu has Rs. 36,000 for purchaes of rice and wheat. A bag of rice and a bag of wheat cost Rs 180 and Rs 120 respectively. He has a storage capacity for 250 bages only. He ears a profit of Rs 11 and Rs. 9 per bag of rice and wheat respectively.
(i) formulate an LPP to maximise the profit
(ii) Solve the LPP.

Condier the following problem. A manufacture produced tables and chairs. It takes 3 hours of work on machine A mind 1 hour of work on machine B to produce one table and 2 hours of work on machine A and 3 hours on machine B to produce 1 chair . He erars a profit fo Rs. 50 per table and Rs 40 per chair. Hoperates the machines a and B for atmost 12 hours hours respectively. how many tables and chairs should be produce each day to maximise his profit ? (i) Write the objective function. (ii) Write the constrains.

A furniture dealer sells only tables and chairs. He has Rs. 12,000 to invest and a space to store 90 pieces. A tables costs him Rs. 400 and a chair Rs 100. He can sell a table at a profit of Rs. 75 and a chair at a profit of Rs. 25. Assume that he can sell the items. The dealer wants to get maximum profit. (i) By defining suitabale variables, write the objective function. (ii) Write the constraints. (iii) Maximise the objective function graphically.

A manufacturer has 3 machines I, II and III installed in his factory. Machines I and II are capable of being operated for utmost 12 hours whereas machine III must be operated atleast for 5 hours a day. He produces only two items A and B each requiring the use of three machines. The number of hours required for producing 1 unit of each of the items A and B on the three machines are given below. He makes a profit of Rs 7600 on item A and Rs 400 on item B. Assume that he can sell all that he produces. (i) Formulate this as a linear programming problem. (ii) Solve the L.P.P by corner point method.

A merchant plans to sell two types of personal computers -a desktop model and a portable model that wil cost Rs. 25,000 and Rs. 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units Determine which the merchant should stock to get maximum profit merchant should stock to get maximum profit if he does not want to invest more than Rs. 70 laksh and if his profit on the dekstop model is Rs 4500 and on portable model is Rs. 5000

A furniture dealer sells only two items namely tables and chairs. He has Rs. 10,000 to invest and a space to store atmost 60 piecs. A table costs him Rs. 500 and a chair rs. 200 He can sell a table at a profit of Rs. 50 and a chair at a profit Rs 15. Assume that he can sell all the items that he buys. By defining suitable variables. i. write the objective function ii. write the cost constraint iii. write the space constraint iv write the non negative constraint

Every gram of wheat provides 0.1g of proteins and 0.25g of carbohydrates. The corresponding values of rice are 0.05g and 0.5g respectively. Wheat costs Rs 2 per kg and rice Rs 8. The minimum daily requirements of protein and carbohydrates for an average child are 50g and 200g respectively. In what quantities, should wheat and rice be mixed in the daily diet to provide the minimum daily re-quirement of protein and carbohydrates at minimum cost.

A manufacturing company makes tow models A and B of product. Each piece of model A reqwuires 9 labour hours for fabricating and 1 hour labour for finishing . Each piece of model Brequires 12 labour hours for fabricating and 3 labour hours for fininshing. for fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs. 8,000 on each piece of modle A and Rs 12,000 on each piece of model B. How many pieces of model A and B should be manufactured per week to realise a maximum profit ? What is the maximum profit per week ?

A tyre manufactureing company produces tyres of cars and buses. Three machines A, B, C are to be used for the production of these typres. Machines A and C are available for operation atmost 11 hours, whereas B must be operated for atleast 6 hours a day. the time required for construction of one typre the three machines given in the following table. Comapy sells all the tyres and gets a profit of Rs. 100 Rs 150 on a tyre of a car and bus respectively. The company wants to know how many numbers of each item to be produced to maximise the profit. To formulate a linear programmining problem, (i) Write the objective function. (ii) Write all constraints.

(Allocation problem) A cooperative society of farmers has 50 hectare of land to grow two crops X and Y. The profit from crops X and Y per hectare are estimated as rs. 10,500 and Rs. 9,000 respectively. To control weeds, a liquid herbicide has to be used for crops X and Y at rates of 20 litres and 10 litres pre hectare. Further, no more than 800 litres of herbicide should be used in order to protect fish and wild life using a pond which collects drainage from this land. How much land should be allocated to each crop so as to maximise the total profit of the society?