Math 1324 Lab 2 - Chapter 3 1.) Matrix A contains the price information for 3 products: T-shirts, Hats, and Shorts. products A price 10 15 20 Matrix B contains sales figures for the three products for 5 days. The rows represent the three products, and the columns represent the number of each product that was sold each day. nbr sold 3 4 12 10 7 B products 4 5 0 5 6 1 3 4 8 3 a.) Write out the 2 matrices, with the correct matrix multiplication (order) that would give a matrix that represents the total revenue for each of the 5 days. b.) What was the total revenue on the last day? _______________ Math 1324 Lab 2 - Ch 3 Page 1 2.) The four departments of Stagg Enterprises need to order the following amounts of the same products. Department 1 Department 2 Department 3 Department 4 Paper 10 7 4 0 Tape 4 2 5 3 Ink cartridges 3 2 1 4 Memo pads 5 3 0 5 pens 6 8 10 5 The unit price (in dollars) of each product is as follows for two suppliers: Product Paper Tape Ink cartridges Memo pads pens Supplier A 9 6 24 4 8 Supplier B 12 6 18 4 12 a.) Use matrix multiplication to get a matrix showing the comparative costs for each department for the products from the two suppliers. WRITE out the matrices in the correct order before using your calculator to find the result. b.) What is the cost of Dept 3's supplies if they buy from Supplier A? c.) Find the TOTAL cost to buy products from each supplier. From which supplier should the company make the purchase? Math 1324 Lab 2 - Ch 3 Page 2 3.) A minor league baseball park has 7000 seats. Box seats cost $6, grandstand seats cost $4, and bleacher seats cost $2. When all seats are sold, the revenue is $26,400. If the number of box seats is one-third the number of bleacher seats, how many seats of each type are there? Give a complete sentence explaining what your answers mean. a.) Clearly define the variables in this problem: x= y= z= b.) Write the equations for this problem. c.) Solve using the Gauss-Jordan method. Show work as indicated in class. Math 1324 Lab 2 - Ch 3 Page 3 4.) A furniture company makes loungers, chairs, and footstools out of wood, fabric, and stuffing. The number of units of each of these materials needed for each of the products is given in the table below. How many of each product can be made if there are 1110 units of wood, 880 units of fabric, and 660 units of stuffing available? Lounger Chair Footstool Wood 40 30 20 Fabric 40 20 10 Stuffing 20 20 10 a.) Clearly define the variables in this problem: x= y= z= b.) Write the equations for this problem. c.) Solve the system of equations using using the inverse matrix. For each create the matrix equation in the form A X = C. Show steps in solving the matrix equation, including A-1 (inverse of the A matrix). Clearly show the final solution matrix. . d.) State your solution in terms of the problem. Math 1324 Lab 2 - Ch 3 Page 4