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Applications of Mathematics 12 Matrices Problem Solving with Matrices Problem 1: The table below shows the standings for three local hockey teams: Team Wins Ties Losses Blazers 7 2 4 Hawks 5 1 7 Tigers 8 0 5 There are two scoring methods: Method 1 Win = 2 points Tie = 1 point Loss = 0 points Method 2 Win = 3 points Tie = 2 point Loss = 1 points Calculate the points for each team using each method. Show the calculations. Method 1: Blazers Hawks Tigers Method 2: Blazers Hawks Tigers page 1 Applications of Mathematics 12 Matrices NOW : Let’s solve the same problem using Matrices : Matrix A = Matrix B = Matrix C = Dimensions of A = Dimensions of B = Dimensions of C = Calculate A B and explain the meaning of your answers Calculate A x C page 2 Applications of Mathematics 12 Matrices Problem 2: A company makes wooden toys. The toys must be cut and assembled. The table below shows the labour hours for each toy. Cutting hours Assembling hours Train 0.5 0.6 Boat 0.4 0.4 Plane 0.2 0.5 The company has an order for 500 trains, 300 boats, and 550 planes. Use matrix multiplication to determine the total cutting time and the total assembling time needed to make the order. If it costs $12.00 an hour for cutting and $ 9.00 an hour for assembling, what will be the total cost for this order? page 3 Applications of Mathematics 12 Matrices Problem 3: SoftSell Corp. sells software at three locations. The sales at each location for different categories of software are given for a 1 week period. Entertainment Business Educational Location 1 200 50 120 Location 2 300 100 50 Location 3 250 150 200 Entertainment software costs $60 each, business software costs $80 each, and educational software costs $75 each. Use matrix multiplication to find the total revenue for each location. page 4 Applications of Mathematics 12 Matrices Problem 4: The following table shows prices at three grocery stores: Item Saveway IMA Supershop Milk 1L $1.13 $1.19 $1.21 Bread 1 loaf $1.09 $1.12 $0.99 Eggs 1 dozen $1.22 $1.35 $1.33 Soup 1 can $0.55 $0.45 $0.60 Three customers want to place orders. Person 1 wants to buy 5L of milk, 3 loaves of bread, 2 dozen eggs and 6 cans of soup. Person 2 wants to buy 2L of milk, 5 loaves of bread, 3 dozen eggs, and 4 cans of soup Person 3 wants to buy 3L of milk, 5 loaves of bread, 4 dozen eggs and 5 cans of soup Use matrix multiplication to determine the total costs for each of these three orders for each store. Assignment : You may use your calculator for the matrix operations. Please write down your steps clearly. CHECK YOUR ANSWERS !!!!! Textbook page 55 # 1, 6,7 page 64 #1 to 7 page 5