Manufacturer can sell x items at a price of rupees `(5-x/(100))`each. The cost price of x items is Rs `(x/5+500)`. Find the number of items he should sell to earn maximum profit

Manufacturer can sell x items at a price of rupees (5-(x)/(100)) each. The cost price of x items is Rs. ((x)/(5)+500) . Find the number of items he should sell to earn maximum prodit.

A dealer wants to purchase 5 litres oil tin and 1 kg ghee tin. He has only Rs. 5760 to invest and has a space for atmost 20 tins. 5 l oil tin costs him Rs. 360 and 1 kg ghee tin costs him Rs. 240. He can sell oil tin at a profit of Rs. 22 and ghee tin at a profit of Rs. 18. Assuming that he can sell all the items that he buys, how should he invest his money for maximum profit ?

Represent the folloowing situations in the form of quadratic equations : (1) The length of the hypotenus of an isosceles right angled triangle is 10 cm. We need to find the length of each of two equal sides. (2)The sum of squares of two consecutive odd positive integers in 970. We need to find those integers. (3) While selling an article for Rs. 96, the profit in percentage is equal to its cost price in rupees. We need to find the cost price of the article. (4) When there is a decreases of 10 km/h in the usual speed of a train, it takes 4(1)/(2) hours more to cover 900km. We need to find the usual speed of the train. (5) The sum of squares of two parts of 31 is 481. We need to find those two parts.

A wholesale dealer wants to starts the business with Rs. 2,40,000. The cost price of a quintal wheat is Rs. 2000 and the cost price of a quintal rice is Rs. 3000. He has the space capacity for 200 quintals grain. The profit from the sale of one quintal wheat is Rs. 125 and that from one quintal rice is Rs. 200. If he has x quintal rice and y quintal wheat then the objective function for the maximum profit is ............

A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs. 7 and screws B at a profit of Rs. 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit ? Determine the maximum profit.

A man owns a field of area 1000 sq.m. He wants to plant fruit trees in it. He has a sum of Rs. 1400 to purchase young trees. He has the choice of two types of trees. Type A requires 10 sq.m. of ground per tree and costs Rs. 20 per tree and type B requires 20 sq.m. of ground per tree and costs Rs. 25 per tree. When fully grown type A produces an average of 20 kg. of fruit which can be sold at a profit of Rs. 2/ - per kg and type B produces an average of 40 kg of fruit which can be sold at a profit of Rs. 1.50/ - per kg. How many of each type should be planted to achieve maximum profit when the trees are fully grown ?

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 should 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.

(Manufacturing problem) A manufacturer has three machines I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for atleast 5 hours a day. She produces only two items M and N each requiring the use of all the three machines. The number of hours required for producing 1 unit of each of M and N on the three machines are given in the following table : She makes a profit of Rs. 600 and Rs. 400 on items M and N respectively. How many of each should she produce so as to maximise her profit assuming that she can sell all the items that she produced? What will be the maximum profit ?

Find the zero of each of the following polynomials : p(x) = 3x + 5

A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5760 to invest and has space for atmost 20 items. A fan costs him Rs. 360 and a sewing machine Rs. 240. His expectation is that he can sell a fan at pofit of Rs. 22 and a sewing machine at a profit of Rs. 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximise his profit ?