12:43 # GH MX SGE Will 12:44 # CH M X B SGE Ill 18. [-/1 Points] DETAILS HARMATHAP11 3,4.025. MY NOTES ASK YOUR TEACHER The inverse of matrix A is given. 22. [-/1 Points] DETAILS HARMATHAP11 3.5.011.MI. MY NOTES ASK YOUR TEACHER [3 21] 4-1= 1 1 2 suppose a primitive economy consists of two industries, farm products and farm machinery. Suppose also that its tec ology matrix is [1 2 1] represented by the matrix shown below. Use the inverse to solve for X. P M 1= 0.2 04 Machinery If surpluses of 84 units of farm products and 10 units of farm machinery are desired, find the gross production of each industry. products units machinery units 23. [-/1 Points] DETAILS HARMATHAP11 3.5,026.MI. MY NOTES ASK YOUR TEACHER Within a company there is a (micro)economy that is monitored by the accounting procedures, In terms of the accounts, the various departments "produce" costs, some of which are internal and some of which are direct costs. This problem shows how an open 19. [-/1 Points] DETAILS HARMATHAP11 3.4.037. MY NOTES ASK YOUR TEACHER Leontief model can be used to determine departmental costs. Use inverse matrices to find the solution of the system of equations. The sales department of an auto dealership charges 10% of its total monthly costs to the service department, and the service department charges 20% of its total monthly costs to the sales department. During ag arunent. During a given month, the direct costs are $83.200 for sales 13 - X3 - 1.5x4 - 0.515 - -74 and $29,400 for service. Find the total costs of each department. (Hound your answers to the nearest whole number.) 0.2515 = 0.675 sales department D.5x1 - 12 + 23 + service department $ 0.512 - 0.5x4 + 0.65 - -0.15 24. [-/1 Points] DETAILS HARMATHAP11 3.5.038. MY NOTES ASK YOUR TEACHER The following problem refers to a closed Leontief model 20. [-/1 Points] DETAILS HARMATHAP11 3.4.061. MY NOTES ASK YOUR TEACHER A closed model for an economy identifies government, the profit sector, the nonprofit sector, and households as its industries. Each unit of government output requires 0.3 unit of government input, 0.2 unit of profit sector input, 0.2 unit of nonprofit sector input, and 0.3 unit Set up the system of equations and then solve it by using an inverse matrix. of households input. Each unit of profit sector output requires 0.2 unit of government input, 0.3 unit of profit sector input, 0.1 unit of nonprofit sector input, and 0.4 unit of households input. Each Suppose that during the first 2 weeks of a controversial art exhibit, the daily number of visitors to the gallery turns out to be the sum of profit sector input, 0.2 unit of nonprofit sector input, and 0.6 unit of households input. Each unit of households output requires the numbers of visitors on the previous 3 days. We represent the numbers of visitors on 3 successive days by 0.05 unit of government input, D.1 unit of profit sector input, D. 1 unit of nonprofit sector input, and 0.75 unit of households input. (a) Write the technology matrix T for this closed model of the economy. 1 Government () Find the matrix M such that Profit Sector MN - Nonprofit sector Households (b) Find the the gross production for each industry. (Let H represent the number of household units produced, and give your answers in terms of H.) SEE government units roth sector units (b) If the numbers of visitors on 3 successive days are given by nonprofit sector units units use M" to find the number of visitors 1 day earlier (before the 173-visitor day). visitors 25. [-/1 Points] DETAILS HARMATHAP11 3.5.042. MY NOTES ASK YOUR TEACHER 21. [-/1 Points] DETAILS HARMATHAP11 3.5.003.MI. MY NOTES ASK YOUR TEACHER A log carrier has a body made from a 4-ft length of reinforced cloth having a patch on each side and a dowel slid through each end to act as handles. The parts-listing matrix for the log carrier is given by the matrix shown below. The following technology matrix describes the relationship of certain industries within the economy to each other. (A&F, agriculture and food, RM, raw materials; M, manufacturing, F, fuels industry, U, utilities; $1, service industries) LC B H C P ARF RM F SI 0 0 0 0 0 Log carrier 0 410 0:008 9602 0 006 ASF 2 0 0 0 0 Handles 8:075 0.006 0.082 8009 0.001 0.416 8 2 0 0 a Patch 40 4053 0.008 0.093 F ow many of each primary assembly item are required to fill an order for 500 log carriers and 20 handles? 0012 0.0102 0 handles cloths For each 1000 units of raw materials produced, how many units of agricultural and food products were required? units patches O III O <