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Chapter 2 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences
- A 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_forwardWrite each system of linear equations as an augmented matrix: (a) {11x=9y57x+5y=1 (b) {5x3y+2z=52xyz=43x2y+2z=7arrow_forwardWrite the augmented matrix of the following system of equations. System {x+yz=1x+2z=32yz=3 Augmented matrixarrow_forward
- Solve for x and y in the matrix equation 2AB=I, given A=[1123] and B=[x2y5].arrow_forwardDetermine whether the matrix is in row-echelon form. If it is, determine whether it is in reduced row-echelon form. 1024011130000arrow_forwardWrite each system of linear equations as an augmented matrix. 376. {3xy=12x+2y=5arrow_forward
- Gasoline 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_forwardWrite the system of equations that that corresponds to the augmented matrix. 200. [2113|42]arrow_forwardSolve for x,y,z and w in the matrix equation wxyx=-432-1+2ywzx.arrow_forward
- Determine the dimension of the matrix 14710238.arrow_forwardProfit: At a local store, the numbers of gallons of skim milk, 2% milk, and whole milk sold over the weekend are represented by A. Skim2%WholemilkmilkmilkA=406452608276769684FridaySaturdaySunday The selling prices per gallon and the profits per gallon for the three types of milk are represented by B. SellingProfitProfitB=$3.45$1.20$3.65$1.30$3.85$1.45Skimmilk2%milkWholemilk (a) Compute AB and interpret the result. (b) Find the store’s total profit from the milk sales for the weekend.arrow_forwardUse 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_forward
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