question_answer 1)

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, Re.1.50 and Re.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 Re.2.00, Re.1.00 and 50 paise respectively, find the gross profit.  

Answer:

Let a row matrix A = [10000   20000   180000] represents annual sale of product in market I and B  represents annual sale of products in market II. (a)   Let a column matrix  represents a unit sale price of product x, y and z.        Total revenue in the market I = AC             = [1000 × 2.50 × 2000 × 1.50 + 18000 × 1.00]       = 25000 + 3000 + 18000 = 46000        Total revenue in the market I = Rs.46,000                    Also, total revenue in the market II = BC             = [6000   2000   8000]                         = 15000 + 3000 + 8000 = 53000              Total revenue in the market II = Rs.53000 (b)   Let a column matrix  represents a unit cost.        Total cost of commodities sold in market                               I = AD             [1000 × 2.00 + 2000 × 1.00 + 18000 × 0.50 ]       = 20000 + 2.00 + 9000 = 31000        Gross profit = Rs.(46,000 ? 31,000) = Rs.15,000.       Also, total cost of commodities sold in market II = BD             = [6000 × 2.00 × 2000 × 1.00 + 8000 × 0.50]       = 12000 + 20000 + 4000 = 36000        Gross profit = Rs.(53000 ? 36000)       = Rs.17,000              Gross profits are Rs.15,000, Rs.17,000