 Hi and welcome to the session. I am Shashi. Let us do one question. Question is a manufacturer produces three products XYZ which he sells in two markets. Annual sales are indicated below. Market first has annual sales of 10000, 2000, 1800 for the products XYZ and the second market has the annual sales of 6000, 2000, 8000 for the products XYZ. Now first mark is if unit sale prices of XYZ are rupees 2.50, rupees 1.50 and rupees 1 respectively find the total revenue in each market with the help of the matrix. Now the part of the question is if the unit cost of the above three commodities are rupees 2 to rupees 1 and 50 paisa respectively find the gross profit. Now let us start with the solution. First of all we will represent the sales of the product as a metric notation. So we can write annual sales of product XYZ in two markets are given in a matrix A. A is equal to matrix 10000, 2000, 1800, 6000, 2000, 8000. Now the rows represent the annual sales of the two markets and the columns represent the annual sales of the three products that is XYZ. Similarly we will represent the unit sale prices as metric notation. Now the unit selling prices of XYZ are given in a matrix B as B is equal to matrix 2.50, 1.50, 1. We know total revenue is given by AB so we get total revenue is equal to AB. We will multiply both the matrix to find the total revenue for each market. So we can write matrix 10000, 2000, 1800, 6000, 2000, 8000 multiplied by matrix 2.50, 1.50, 1. Now we will multiply the matrices and get 10000 multiplied by 2.50 plus 2000 multiplied by 1.50 plus 1800 multiplied by 1. This element we have obtained after multiplying the first row with this first column. Now we will multiply the second row with second column and get 6000 multiplied by 2.50 plus 20000 multiplied by 1.50 plus 8000 multiplied by 1. On simplifying we get the matrix 46000, 53000. So total revenue for the first part is given by the matrix 46000, 53000. So we can write total revenue in market first is equal to rupees 46000 and the total revenue in market second is equal to rupees 53000. As we know the rows represent the two markets. Now let us start the B part of the question. B part of the question is if the unit cost of the above three commodities are rupees 2, rupees 1 and 50 paisa respectively find the gross profit. So now let us start with the solution of the B part. The unit cost of the three commodities are given by the matrix C. C is equal to matrix 2, 1.50. Here we were given 50 paisa in the question. So 50 paisa is equal to 0.50 rupees. So that is why we have written here 0.50. Now total cost of each market is equal to AC. We know A is equal to matrix 10000, 2000, 180000, 6000, 2000, 8000 and C we can see this matrix 2, 1, 0.50. Now we can see there are three columns in matrix A and three rows in matrix C. Since the number of columns of matrix A is equal to number of rows of matrix C, so their product is defined. So we can write 10000 multiplied by 2 plus 2000 multiplied by 1 plus 18000 multiplied by 0.5. Second element is 6000 multiplied by 2 plus 20000 multiplied by 1 plus 8000 multiplied by 0.50 matrix. Now on simplifying we get the matrix 31000, 36000. Now we know profit matrix is equal to total revenue matrix minus total cost matrix. We have obtained above in A part total revenue matrix as 46000, 53000 minus total cost matrix is 31000, 36000. Now this is further equal to matrix 15000, 17000. So we can see the profit in market first is equal to rupees 15000 and the profit in market second is equal to rupees 17000. Since the rows represent two markets, so profits are represented by these rows. So our final answer is total revenue in market first is equal to rupees 46000, total revenue in market second is equal to rupees 53000 for the A part and solution for the B part is gross profit in market one is equal to rupees 15000 and gross profit in second market is equal to rupees 17000. This completes the session. Hope you understood the session. Take care and goodbye.