MP3 Sales A store sells three types of MP3 players. Matrix A contains information about size (in gigabytes), battery life (in hours), and weight (in ounces) of the three MP3 players. Matrix B contains the sales prices (in dollars) of the MP3 players, while matrix C contains the number of each type of player sold in one week.
Calculate and interpret the following:
(a) BC
(b) AC
(c) the row 2, column 1 entry of AC
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Finite Mathematics & Its Applications (12th Edition)
- Use matrix methods to solve each problem Nutritional planning One ounce of each of three foods has the vitamin and mineral content shown in the table. How many ounces of each must be used to provide exactly 22 milligrams mg of niacin, 12 mg of zinc, and 20 mg of vitamin C? Food Niacin Zinc Vitamin C A 1 mg 1 mg 2 mg B 2 mg 1 mg 1 mg C 2 mg 1 mg 2 mgarrow_forwardAgriculture A fruit grower raises two crops, apples and peaches. The grower ships each of these crops to three different outlets. In the matrix A=12510075100175125 aij represents the number of units of crop i that the grower ships to outlet j. The matrix B=3.506.00 represents the profit per unit. Find the product BA and state what each entry of the matrix represents.arrow_forwardRevenue: An electronics manufacturer produces three models of high-definition televisions, which are shipped to two warehouses. The shipment levels are represented by A. 12WarehouseA=5,0004,0006,00010,0008,0005,000ABCModel The prices per unit are represented by the matrix B=$699.95$899.95$1099.95. Compute BA and interpret the result.arrow_forward
- Nutrition A nutritionist is studying the effects of the nutrients folic acid, choline, and inositol. He has three types of food available, and each type contains the following amounts of these nutrients per ounce. (a) Find the inverse of the matrix [313424324] and use it to solve the remaining parts of this problem. (b) How many ounces of each food should the nutritionist feed his laboratory rats if he wants their daily diet to contain 10 mg of folic acid, 14 mg of choline, and 13 mg of inositol? (c) How much of each food is needed to supply 9 mg of folic acid, 12 mg of choline, and 10 mg of inositol? (d) Will any combination of these foods supply 2 mg of folic acid, 4 mg of choline, and 11 mg of inositol?arrow_forwardUse matrix methods to solve each problem. Chainsaw sculpting A wood sculptor carves three types of statues with a chainsaw. The number of hours required for carving, sanding, and painting a totem pole, a bear, and a deer are shown in the table. How many of each should be produced to use all available labor hours? Totem Pole Bear Deer Time Available Carving 2 hr 2 hr 1 hr 14 hr Sanding 1 hr 2 hr 2 hr 15 hr Painting 3 hr 2 hr 2 hr 21 hrarrow_forwardA factory manufactures three products (doohickies, gizmos, and widgets) and ships them to two warehouses for storage. The number of units of each product shipped to each warehouse is given by the matrix A=[20015010075100125] (where aij is the number of units of product i sent to warehouse j and the products are taken in alphabetical order). The cost of shipping one unit of each product by truck is $1.50 per doohickey, $1.00 per gizmo, and $2.00 per widget. The corresponding unit costs to ship by train are $1.75, $1.50, and $1.00. Organize these costs into a matrix B and then use matrix multiplication to show how the factory can compare the cost of shipping its products to each of the two warehouses by truck and by train.arrow_forward
- Agriculture: A farmer grows apples and peaches. Each crop is shipped to three different outlets. The shipment levels are represented by A. 123OutletA=12510075100175125ApplesPeachesCrop The profits per unit are represented by the matrix B=$3.50$6.00. Compute BA and interpret the result.arrow_forwardGasoline Sales Matrix A shows the numbers of gallons of 87 octane, 89 octane, and 93 octane gasoline sold at a convenience store over a weekend. 878993OctaneA=[5808403205604201608601020540]FridaySaturdaySunday Matrix B gives the selling prices in dollars per gallon and the profits in dollars per gallon for the three grades of gasoline. SellingpriceProfitB=[b110.05b210.08b310.10]878993}Octane (a) Find AB and interpret the result. (b) Find the convenience stores profit from gasoline sales for the weekend.arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning