A manufacturer produces three products x,y,z which he sells in two markets ,Annual sales are indicated below:
`{:("Market",,"products",),(I,"10,000","2,000","18,000"),(II,"6,000","20,000","8,000"):}`
(A) if unit sale prices of x,y and z are Rs. 2.50, Rs. 1.50 and Rs. 1.00, respectively , find the total revenue algebra .
(b) if the unit costs of the above three commodities are Rs. 2.00,Rs. 1.00 and 50 paise respectively, find the gross profit.

Explanation

Let the matrix A respesents the production .
`therefore A=[{:(10000,2000,18000),(6000,20000,8000):}]`
(A) Let the matrix B respesents the selling price per unit ,
`therefore B=[{:(2.50),(1.50),(1.00):}]`
`Now, AB=[{:(10000,2000,18000),(6000,20000,8000):}][{:(2.50),(1.50),(1.00):}]`
`=[{:(25000+3000+18000),(15000+30000+8000):}]=[{:(46000),(53000):}`
`therefore ` Totoal revenue of market I=Rs.46000
Total revenuse of market II =Rs. 53000
(b) Let the matrix C represents the cost per unit.
`therefore C=[{:(2.00),(1.00),(0.50):}]`
`Now,AC=[{:(10000,2000,18000),(6000,20000,8000):}][{:(2.00),(1.00),(0.50):}]`
` =[{:(20000+2000+9000),(12000+20000+4000):}]=[{:(31000),(36000):}]`
profit in market `I=Rs. 46000-Rs. 31000=Rs.15000`
profitr in market `II=Rs. 53000-Rs.36000=Rs.17000`
Total profit `=Rs. 15000+Rs.17000=Rs.32000`