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.

Find the number of solution to equation (log)_2(x+5)=6-x :

Find the number of real solutions to the equation log_(0.5)x=|x| .

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.

Find the number of solutions of equation 2^x+3^x+4^x-5^x=0

Find the number of real solutions of sin (e^x) = 5^x + 5^(-x) .

Find the cardinal number of the following sets. B={x:x inW,xle5} .

The owner of a small restaurant can prepare a particular meal at a cost of Rupees 100. He extimate that if the menu price of the meal is x rupees, then the number of customers who will order that meal at that price in an evening is given by the function D (x) = 200 - x. Express his day revenue total cost and profit on this meal as a function of x.

The owner of a small restaurant can prepare a particular meal at a cost of Rupees 100. he estimates that if the menu price of the meal is x rupees, then the number of customers who will order that meal at that price in an evening is givenby the function d(x) = 200 - x. Express his revenue, total cost and profit on this meal as functions of x .

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 its 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.