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A manufacturer produces three product...

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 1.0

Text Solution

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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`
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