Concept explainers
Input-Output Closed Model Use the input-output matrix
and the closed model to find the ratio of coal to steel produced.
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Finite Mathematics (11th Edition)
- Determine whether the matrix is in row-echelon form. If it is, determine whether it is in reduced row-echelon form. 1024011130000arrow_forwardSolve the homogeneous linear system corresponding to the coefficient matrix. [121200242412]arrow_forwardCAPSTONE In your own words, describe the difference between a matrix in row-echelon form and a matrix in reduced row echelon form. Include an example of each to support your explanation.arrow_forward
- A manufacture produce three models of a product and ships them to two warehouse. In the matrix A=[200300600350250400] aij represent the number of units model i that the manufacturer ships to warehouse j. The matrix B=[12.509.0021.50] Represent the price of the three models in dollars per unit. Find the product BA and state what each entry of the matrix represents.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_forwardSolving for the Output Matrix A small community includes a farmer, a baker, and a grocer and has the input-output matrix D and external demand matrix E below. FarmerBakerGrocerD=[0.40.50.50.30.00.30.20.20.0]FarmerBakerGrocer and E=[100010001000] Solve for the output matrix X in the equation X=DX+E.arrow_forward
- Agriculture 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_forwardReferring to Exercise 19, suppose that the unit cost of distributing the products to stores is the same for each product but varies by warehouse because of the distances involved. It costs $0.75 to distribute one unit from warehouse 1 and $1.00 to distribute one unit from warehouse 2. Organize these costs into a matrix C and then use matrix multiplication to compute the total cost of distributing each product.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
- 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_forwardAgriculture: 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_forwardNutrition 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_forward
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