The total population of a tropical island is 200 people. Every day each person either goes fishing or gathers fruit. All food is shared between the islanders and none is traded outside the island. The production of 5 units of fish requires four people and one unit of fish. The production of 1 unit of fruit requires one person. Each person in the island requires 2/5 units of fish and 3/5 units of fruit. (a) Write the input-output matrix A for the closed Leontief economic model which describes this island. Hint: the sectors are fish, fruit and people (labour). (b) Solve the closed Leontief economic model using Gauss-Jordan elimination by hand, showing working, to find the production vector. (c) On this island, how many people go fishing and how many people gather fruit?

only HANDWRITTEN answer needed ( NOT TYPED)

Two departments of a firm, A and B, need differing amounts of steel, wood, and plastic. The table on the right gives the amount of each product the departments need. These three products are supplied by two suppliers, Company C and Company D, with the unit prices given in the table on the right. a. Use matrix multiplication to determine how much these orders will cost each department at each of the two suppliers. Enter the amounts into the cost matrix shown on the right. Department A Department B Steel Wood Plastic Dept. A Dept. B Company C 600 310 310 Co. C Steel Wood Plastic 60 40 40 60 70 60 Company D 560 190 390 Co. D

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise In the matrix shown below, form a row-equivalent matrix by multiplying row 1 by -6 and adding the result to row 2. In other words, apply the row operation (R₂-6R₁) to the given matrix. -8 5 5 1 6 84 5 Step 1 Perform elementary row operations to form a row-equivalent matrix. Add -6 times row 1 to row 2 and put the result in row 2. 1 1 -8 5 6 5 1 8 4 5 R₂-6R₂ -6(1) 5- -8 (-8) 1-6 5 8 -4 5 Simplifying all values gives the following matrix, which is row-equivalent to the original matrix.