9. Suppose that three industries are interrelated so that their outputs are used as inputs bythemselves, according to the 3 x 3 consumption matrix A below, where ajk is the fraction of theoutput of industry k consumed (purchased) by industry j. Let p; be the price charged by industry jfor its total output. Your mission is to find nonnegative prices p = [p1, p2 , p3] so that for eachindustry, total expenditures equal total income. Show the details of your work.0.10.4P1A = [a] = 0.8 00.7P= P20.10.60.3P3

Answered: 9. Suppose that three industries are…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 24EQ: Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry...

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23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.
Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry requires $0.30 of coal and $0.70 of steel. Every $1 produced by steel requires $0.80 of coal and $0.20 of steel. Find the annual production (output) of coal and steel if the total annual production is $20 million.
2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1
A rental car company has an imbalance of cars at seven of its locations. The following net- work shows the locations of concern (the nodes) and the cost to move a car between loca- tions. A positive number by a node indicates an excess supply at the node, and a negative number indicates an excess demand.
1. A company produces two colors of cloth, namely red and pink. In order to produce these colors, 2 special raw materials are being used by the company. The production data is given below: Meters of raw material per meter of Maximum daily availability Red Cloth Pink Cloth Raw Material 1 2 1 6 Raw Material 2 4 24 Profit per ton (1000) According to the dealer, the daily maximum demand for red cloth is 2 meters and the daily demand for red cloth can't exceed that for pink cloth by more than 1 meter. The company wants to maximize its daily profit. a. Construct the LP Model of this problem. b. Find the optimal solution using Graphs. (graphing paper or desmos) c. Find the optimal solution using Excel Solver. (Sheet 1) d. Find the optimal solution using Algebraic Solution. e. Find the optimal solution using the Simplex Method. (Not in excel)
A factory manufactures three products. These products are processed through 3 different conduction stages. The time required to manufacture each of these 3 products and the daily capacity of the stages are given by the following data Time per unit (minutes) stage Product 1 Product 2 Product 3 Stage capacity min/day 1 1 1 430 2 3 2 460 3 1 4 420 Use simplex method to determine the daily number of units to be manufactured of each product given that the profit per unit for product 1, 2 and 3 are 3, 2 and 5 respectively. Assume that all amounts produced are consumed by the market. Fully interpret your solution.
The monthly income associated with the sale of two products is described with the function in two variables / = 21a + 19b, where a and b are quantities sold of products A and B, respectively. Furthermore, it is known that the cost of producing these products is modeled by C = 3a² +6b². With this information answer: Write the criterion of the monthly profit function from the sales of products A and B, use as variables a and b What is the only critical point of the utility function? What is the value of the discriminant of the utility function evaluated at that critical point (Value of D used to classify the critical point) At this critical point. Is a relative maximum, a relative minimum, or neither determined?
A manufacturing company has three processing lines. Each processing line combines various raw materials to produce the same output, Y. One of the processing lines can combine units of input (X) to produce units of output (Y) such that there is a linear relationship between X and Y. The Chief Executive Officer wants the output model to be estimated for this processing line. Given the values of X and Y (in thousands of units) in the table below, and as the Director of Data Management, you are to: x 5 7 2 8 4 8 12 6 14 8 Determine the extent to which output changes as the input change and interpret your result. Find the intercept of the output model and interpret it. Write down the equation of the line of best fit for output. Determine the value of the extent of relationship between input (X) and output (Y), and interpret your result.
Suppose that the supply and demand sets for a particular market are given byS = { (q,p) | 3p - q = 5 } and D = { (q,p) | 3p + q2 + 2q = 9 } .a. Determine the supply function qS, the demand function qD, and state clearly the domain and range of each.b. Determine the inverse supply function pS, and the inverse demand function pD, and state clearly the domain and range of each
6) The following data is available for a simple hedonic home price model. Lot size and house size are continuous variables. For example, for every 100 square feet in house size, the value of the home increases by $150x100=15,000. Regarding proximity to a hospital, any home within 3 miles of a hospital is worth an additional $10,000 premium. Beyond 3 miles, there is no premium. What is the value of a 2,000 square foot home on a 5,000 square foot lot 2 miles from the hospital? Coefficient Value Description Lot size in Sq Ft House in Sq Ft Within 3 Miles of Hospital 60 150 10,000
A farmer has recently acquired a 110 hectares piece of land. He has decided to grow Wheat and barley on that land. Due to the quality of the sun and the region's excellent climate, the entire production of Wheat and Barley can be sold. He wants to know how to plant each variety in the 110 hectares, given the costs, net profits and labor requirements according to the data shown below: Variety Cost (Price/Hec) Net Profit (Price/Hec) Man-days/Hec Wheat 100 50 10 Barley 200 120 30 The farmer has a budget of US$10,000 and an availability of 1,200 man-days during the planning horizon. In addition, the farmer would like to get a profit of at least $3000. Generate the mathematical model for the optimal usage of land area to produce wheat and barley. Using graphical method to optimize land usage, how many hectares are to be used for wheat and barley.
Suppose that the market for air travel between Chicago and Dallas is served by just two airlines, United and American. An economist has studied this market and has estimated that the demand curves for round-trip tickets for each airline are as follows: Qu = 10,000 - 100Pu + 99Pa (United's Demand); Qa = 10,000 - 100Pa + 99Pu (American's Demand) where Pu is the price charged by United, and Pa is the price charged by American. What is the market-level price elasticity of demand for air travel between Chicago and Dallas when both airlines charge a price of $300?

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