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

A factor 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 maufacture a package of screw s A, while it take 6 minutes on automatic and 3 minutes on the hand operated machines to maufacture 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 screw he manufactures, how many packages of each type should the factory owner produced day in order to maximise his profit? Determine the maximum profit.

A cement company earns a profit of 8 rs per bag of white cement sold and a loss of rs. 5 per bag of gray cement sold. :- What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is rs 6,400 bags.

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 excced 250 units . Determine tha number of units of each type of computer which the 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 desktop model is Rs 4500 and on portable model is Rs 5000.

The angles of a triangle are (2x)^(@), (3x + 5)^(@) and (4x − 14)^(@) . Find the value of x and the measure of each angle of the triangle

Find the real numbers x and y if (x-iy) (3+5i) is the conjugate of -6 - 24 i .

Two slits 0.3mm apart are illuminated by light of wavelength 4500Å . The screen is placed at 1m distance from the slits. Find the separation between the second bright fringe on both sides of the central maximum. Data : d=0.3mm=0.3xx10^(-3)m , lambda=4500Å=4.5xx10^(-7)m , D=1m , n=2 , 2x=?

A furniture dealer deals in only two items - tables and chairs. He has Rs. 50,000 to invest and has storage pince of at most 60 pieces. A table costs Rs. 2500 and a chair Rs. 500. He estimates thnt from the sale of one table , he can make a profit of Rs. 250 and that from the sale of one chair a profit of Rs. 75. How many tables and chairs he should buy from the available money so as to maximise his total profit assuming that he can self all the items which he buys.

The total cost C(x) in rupees associated with the production of x units of an item is given by C(x) = 0.007x^(3) - 0.003 x^(2) + 15x + 4000 . Find the marginal cost when x = 17 units are produced.

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = 0.007x^(3) - 0.003x^(3)+15x+4000 . Find the marginal cost when 17 units are produced.