A manufacturer reckons that the value of a machine, which costs him Rs. 15625 , will depreciate each year by `20 %`. Find the estimated value at the end.of 5 years.

Height of a plant at a certain date is 1.6m. Suppose that the height is increased by 5 cms in the following year and the height is increased in each year by half of that in the preceding year. Find the height of the plant at the end of n years.

A man deposited Rs. 10000 in a bank at the rate of 5 % simple interest annually. Find the amount in. 15^ th year since he deposited the amount and also calculate the total amount after 20 years.

A man deposited Rs. 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15^(th) year since he deposited the amount and also calculate the total amount after 20 years.

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:

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs.5 and that from a shade is Rs.3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?

A firm manufactures two types of products A and B and sells them at a profit of Rs. 5 per unit of type A and Rs. 3 per unit of type B . Each product is processed on two machines M_1 and M_2 . One unit of type A requires one minute of processing time, on, M_1 and two minutes of processing time on M_2 whereas one unit of type B requires one minute of processing time on M_1 and one minute of M_2 . Machines M_1 and M_2 are respectively available for at most 5 hours and 6 hours a day. Find how many, units of each type of product should the firm produce a day, in order, to maximise the profit. Solve thè problem graphically.

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 14kg of nitrogen and 14kg 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 ?