A manufacture produces three products x,y,z which he sells in two markets . Annual sales are indicated below :

(a) If unit sale prices of x,yand z are Rs. 2.50, Rs. 1.50 and Rs. 1.00 , respectively, find the total revenue in each market with the help of matrix algebra.
(b) If the unit costs of the above three commodities are Rs. 2.00, Rs. 1.00 and 50 paise repectively .Find the gross profit.

Vector B has x,y and z components of 4.00,6.00 and 3.00 units, respectively. Calculate the magnitude of B and the angle that B makes with the coordinates axes.

The unit of three physical quantities x, y and z are g cm^(2) s^(-5) , gs^(-1) and cm s^(-2) respectively. The relation between x, y and z is

The bookshop of a particular school has 10 dozen chemistry books , 8 dozen physics books, 10 dozen economics books . Their selling prices are Rs. 80, Rs, 60 and Rs.40 each respectively . Find the total amount the bookshop will receive from selling all the books using matrix algebra.

A manufacturer produces two models of bikes model X and model Y. Model X takes a 6 man hours to make per unit, while Model Y takes 10 man-hours per unit. There is a total of 450 man-hour available per week. Handling and Marketing costs are Rs. 2000 and Rs. 1000 per unit for Models X and Y respectively. The total funds available for these purposes are Rs. 80,000 per week. Profits per unit for Models X and Y are Rs. 1000 and Rs. 500, respectively. How many bikes of each model should the manufacturer produce, so as to yield a maximum profit ? Find the maximum profit.

The cost of 4 pens and 4 pencil boxes is Rs. 100. Three times the cost of a pen is Rs. 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box.

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.

The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the celling at the rate of Rs. 7.50 per m^(2) .

The cost of 2 pencils and 3 erasers is Rs. 9 and the cost of 4 pencils and 6 erasers is Rs. 18. Find the cost of each pencil and each eraser.

The area of a circular playground is 22,176 m^(2) . Find the cost of facing this ground at the rate of Rs.50 per meter.