(4) For what values of z is the matrix A invertible?(5) Solve the system of equations in part (2) by Cramer's rule when z = 0.5. Question 2We assume that an economy has only three sectors: Goods, Services and Consumption.The Goods sector has a total annual output of r units, the Services sector has a totalannual output of y units, and the Consumption sector does not produce goods or servicesbut only consumes 18 units of Goods and 11 units of Services annually. Each year, tomeet the consumer demand, for its own production:(i) the Goods sector must use 10% of its own total output and 60% of the total outputfrom the Services sector; and(ii) the Services sector must use 100z% pereent of its own total output and 50% of thetotal output from the Goods sector, where z is an unknown real number between 0and 1.The economy is in equilibrium if for each production sector (of Goods and Services), theoutput is equal to the sum of its input and the consumer demand.(1) Derive a two-equation linear system to demonstrate the relationship between z andy, treating z as an unknown constant.(2) Re-express the above linear system in a matrix form:AShow all the elements of A and b.(3) What is the determinant of matrix A in terms of z (that is, as a function of z)?

Given Information:Economy has three sectors: Good, Services, Consumption.Few information regarding…

Answered: We assume that an economy has only…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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An economy is based on three sectors-agriculture, manufacturing, and services. For each unit of output, agriculture requires inputs of 0.30 unit from agriculture, 0.30 unit from manufacturing, and 0.30 unit from services. For each unit of output, manufacturing requires inputs of 0.30 unit from agriculture, 0.20 unit from manufacturing, and 0.20 unit from services. For each unit of output, services requires 0.20 unit from agriculture, 0.30 unit from manufacturing, and 0.30 unit from services. Determine the production levels needed to satisfy a final demand of 0 units for agriculture, 50 units for manufacturing, and 0 units for services. The production level needed from the agricultural sector is units. (Do not round until the final answer. Then round to two decimal places as needed.)
“A car manufacturer produces two versions of its popular medium sized model: a hatchback aimed at the family market and a coupe designed to appeal to affluent single customers.Both are based on the same chassis and differ only in the body kit used to make up the cars. They are both produced at the same factory.There are 95,000 hours of manpower and 8,900 basic chassis units (one per vehicle) available each week. The hatchback takes 4 hours of assembly time while a coupe takes 6.5 hours.At least 1,000 coupe models should be produced per week.Production is also constrained by the fact that owing to problems with a supplier only 34,000 door handles are available per week. A hatchback uses ten of these handles while a coupe uses four.The profit to the factory on a hatchback model is estimated to be £3,450 while the profit on a coupe is £975.The market demand for the cars is high. It is known that demand will exceed production for time to come so they should be able to sell whatever mix of…
Example 12.8. A firm uses milling machines, grinding machines and lathes to pro- duce two motor parts. The machining times required for each part, the machining times avail- able on different machines and the profit on each motor part are given below : Machining time reqd. for the motor part Max. time available per Type of machine (mts) week (minutes) I II 10 2,000 Milling machines Grinding machines Lathes. 2 900 12 3,000 Profit/ unit (Rs.) 100 40 Determine the number of parts I and II to be manufactured per week to maximize the profit. د ه
Need only a handwritten solution only (not a typed one).
A local firm is planning its workforce and production levels over the next year. The firm makes a variety of microprocessors and uses sales dollars as its aggregate production unit. Based on orders received and sales forecasts provided by the marketing department, the estimate of dollar sales for the next year by month is as follows: Month Production Days Predicted Demand(in $10,000) Month Production Days Predicted Demand(in $10,000) January 20 595 July 20 410 February 19 225 August 21 130 March 22 565 September 19 405 April 18 205 October 23 315 May 21 230 November 21 355 June 22 120 December 18 350 Inventory holding costs are based on a 25% annual interest charge. It is anticipated that there will be 675 workers on the payroll at the end of the current year and inventories will amount to $120,000. The firm would like to have at least $100,000 of inventory at the end of December…
A company is dedicated to the production of different vegetable-flavored milks. Currently the company produces two types of milk: almond and coconut, which it sells at $ 5,000 and $ 2,000 / liter respectively. Milk production is subject to the use of machine hours in the production plant and of water as a fundamental resource. It takes 1 machine-hour and 2 liters of water to produce 1 liter of almond milk, while it takes 3 machine-hours and 1 liter of water to produce 1 liter of coconut milk. The company currently has 100 machine-hours and 50 liters of water to make the milk, and it is also required to make at least 30 liters of milk in total. 1. Set up the linear programming model in standard format.2. Determine all the basic solutions to the problem. Identify which ones are feasible and which ones are not. Analyze what happens graphically.3. Determine an initial feasible basic solution using phase I. In each iteration, write the resulting model in dictionary format and analyze what…
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