(8) Consider an economy consisting of three sectors: food, clothing, and shelter. The productionof 1 unit of food requires the consumption of 0.4 unit of food, 0.2 unit of clothing, and 0.2 unitof shelter. The production of 1 unit of clothing requires the consumption of 0.1 unit of food,0.2 unit of clothing, and 0.3 unit of shelter. The production of 1 unit of shelter requires theconsumption of 0.3 unit of food, 0.1 unit of clothing, and 0.1 unit of shelter. Find the level ofproduction for each sector in order to satisfy the demand for 100 units worth of food, 30 unitsworth of clothing, and 250 units worth of shelter.

We will use the Leontief input-output model. If X represents production vector, A is the matrix of…

Answered: Consider an economy consisting of three…

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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A company produces 3 products. Each unit of product 1, 2, and 3 generate a profit of GH₵10, GH₵12, and GH₵12 respectively. Each product has to go through a manufacturing, assembly, and testing phase. The company’s resources are such that only 20 hours of manufacturing, 20 hours of assembly, and 20 hours of testing are available. Each unit of product 1 has to spend 1 hour in manufacturing, 2 hours in assembly, and 2 hours in testing. Each unit of product 2 has to spend 2 hours in manufacturing, 1 hour in assembly, and 2 hours in testing. Each unit of product 3 has to spend 2 hours in manufacturing, 2 hours in assembly, and 1 hour in testing. Company ABC wants to know how many units of each product it should produce, in order to maximize its profit.a) Formulate a linear programming model for this problem.
A brewery produces regular beer and a lower-carbohydrate "light" beer. Steady customers of the brewery buy 12 units of regular beer and 18 units of light beer monthly. While setting up the brewery to produce the boors, the management decides to produce extra beer, beyond that needed to satisfy customers. The cost por unit of regular beer is $32,000 and the cost per unit of light beer is $60,000. Every unit of reqular beer brings in $100,000 in revenue, while every unit of light beer brings in $300,000 in revenue. The brewery noeds at least $9,000,000 in revenue, and has determined that the total demand will be at least 50 units of beer. Complete parts (a) and (b). (a) How much of each type of beer should be made so as to minimize total production costs? 30 units of regular beer and 20 units of light beer should be made, for a minimum total cost of $ 2160000 (Type integers or decimals.) (b) Suppose the minimum revenue is increased to $9,400,000. Use shadow costs to calculate the total…
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