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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 18.000II 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 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 50paise respectively. Find the gross profit. |
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Answer» Let `A` is the matrix that represents annual sales for both markets. `A = [[10000,2000,18000],[6000,20000,8000]]` (a) Let `B` is the matrix that represents unit sale prices of the products. Then, `B = [[2.5],[1.5],[1]]` `:.` Revenue ` = AB = [[10000,2000,18000],[6000,20000,8000]] [[2.5],[1.5],[1]]` `=>AB = [[10000**2.5+2000**1.5+18000**1],[6000**2.5+20000**1.5+8000**1]] = [[46000],[53000]]` (b) Let `C` is the matrix that represents unit cost prices of the products. Then, `C = [[2],[1],[0.5]]` So, the cost price `= AC = [[10000,2000,18000],[6000,20000,8000]] [[2],[1],[0.5]]` `=>AC = [[10000**2+2000**1+18000**0.5],[6000**2+20000**1+8000**0.5]]= [[31000],[36000]]` `:.` Gross Profit `= AB -AC = [[46000],[53000]] - [[31000],[36000]] = [[15000],[17000]]` |
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