A simplified economy involves just three commodity categories agriculture, manufacturing, and transportation, all in appropriate units.Production of 1 unit of agriculture requires 1/5 unit of manufacturing and 1/3 unit of transportation; production of 1 unit of manufacturingrequires 1/3 unit of agriculture and 1/3 unit of transportation; and production of 1 unit of transportation requires 1/4 unit of agriculture and1/3 unit of manufacturing. If the demand is 624 units of each commodity, how many units of each commodity should be produced?Find the input-output matrix, A, and the demand matrix, D, for this economy.The input-output matrix is(Type an integer or fraction for each matrix element.)

Answered: Image /qna-images/answer/15fb4acf-3ea6-4d93-a3d4-df3712fdca76.jpg

Answered: A simplified economy involves just…

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 factory manufactures two products, A and B. Each product requires the use of three machines, Machine I, Machine II, and Machine III. The time requirements and total hours available on cach machine are listed below. Machine I Machine II Machine III Product A 1 2 4 Product B 2 2 2 Total hours 70 90 160 Table 6.1 If product A generates a profit of $60 per unit and product B a profit of $50 per unit, how many units of cach product should be manufactured to maximize profit, and what is the maximum profit?
A manufacturer can sell product 1 at a profit of $2/unit and product 2 at a profit of $5/unit. Three units of raw material are needed to manufacture 1 unit of product 1, and 6 units of raw material are needed to manufacture 1 unit of product 2. A total of 120 units of raw material are available.If any of product 1 is produced, a setup cost of $10 is incurred, and if any of product 2 is produced, a setup cost of $20 is incurred. Formulate an IP to maximize profits.
A company uses four special tank trucks to deliver four different gasoline products to customers. Eachtank has five compartments with capacities: 500, 750, 1200, 1500, and 1750 gallons. The daily demands forthe four products are 10000, 15000, 12000, and 8000 gallons. Any quantities that cannot be delivered by thecompany’s four trucks must be subcontracted at the additional costs of 5, 12, 8, and 10 cents per gallon forproducts 1, 2, 3, and 4, respectively. The goal is to develop the optimal daily loading schedule for the fourtrucks that will minimize the additional cost of subcontracting. Formulate this problem as an integer linearprogram, and solve it using linear program solver.
XYZ Corporation operates two plants, each of which has a capacity of 200 units per day. Each day, XYZ must ship their product to each of four customers. Customers A, B, and C each have a demand of 17 units per day while customer D has a demand of 349 units per day. The cost of shipping one unit of each product from each of the two plants to each of the customers is shown in the table below. Customer A Customer B Customer C Customer D Plant 1 25 19 12 14 Plant 2 15 21 23 20 How many units should XYZ ship from each plant to each customer?
kindly answer items (d) and (e)
Firms Alpha and Beta serve the same market. They have constant average costs of $2 per unit. The firms can choose either a high price ($10) or a low price ($5) for their output. When both firms set a high price, total demand is 10,000 units which is split evenly between the two firms. When both set a low price, total demand is 18,000, which is again split evenly. If one firm sets a low price and the second a high price, the low priced firm sells 15,000 units, the high priced firm only 2,000 units. Analyze the pricing decisions of the two firms as a non-cooperative game. Derive the dominant strategy equilibrium of this game. Explain why this is an example of the prisoners’ dilemma game.

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