Qa) and b). Given an exchange table for the economy that consists of three sectors.Distribution of Output from:TransportationManufacturingServicesPurchased by:0.30.8Transportation0.50.10.1Manufacturing0.50.60.1ServicesDenote the total annual output (in dollars) of the transportation, manufacturing and servicessectors by Pr» PMandPs, respectively.(a) Formulate a homogeneous system of linear equations to describe the income/expensesrequirements for the sectors.(b) Write (a) as a single matrix equation.(c) Solve (a) by applying Gauss-Jordan elimination method.(d) Using the result obtained in (c), what is the set of equilibrium prices for the sectors whenthe service sector has an annual output of $80?

Answered: Image /qna-images/answer/5b660303-1b72-4383-abee-945efeafd7d0.jpg

Answered: Given an exchange table for the economy…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A company that has cement factories in Denizli, İzmir and Uşak will transport the cements to theconsumption region 1, 2 and 3. The cement production capacities of the factories are 200 tons forthe factory in Denizli, 300 tons for the factory in İzmir and 450 tons for the factory in Usak.Demand of the first consumption region is 250, demand of the second region is 100, demand of thethird region is 225 and demand of fourth region is 325 tons of cement. The transportation costbetween factories and consumption areas is as below table per ton:Factories 1. Region 2. Region 3. Region 4. RegionDenizli 15 18 12 13İzmir 10 10 11 9Usak 8 5 7 8According to these data;1) Make the initial distribution of the enterprise according to the Vogel’s Approximation Method(VAM) and calculate the total transportation cost. 2) Determine the distribution that minimizes the total transportation cost according to the (MODI)method.
Suppose an economy has only two sectors: Goods and Services. Each year, Goods sells 80% of its outputs to Services and keeps the rest, while Services sells 68% of its output to Goods and retains the rest. Find equilibrium prices for the annual outputs of the Goods and Services sectors that make each sector's income match its expenditures. Denote the prices (that is, dollar values) of the total annual outputs of the Goods and Services sectors by pG and pS,respectively.
The Center for Information Technology at State Univer-sity has outgrown its office in Bates (B) Hall and is mov-ing to Allen (A) Hall, which has more space. The move will take place during the three-week break between the end of summer semester and the beginning of fall semes-ter. Movers will be hired from the university’s physical plant to move the furniture, boxes of books, and files thatthe faculty will pack. The center has hired a local retailcomputer firm to move its office computers so they willnot be damaged. Following is a list of activities, theirprecedence relationships, and probabilistic time estimatesfor this project:Determine the earliest and latest start and finish times, thecritical path, and the expected project duration. What is theprobability the center will complete its move before thestart of the fall semester?
Assuming an M/M/1 system setup with a service rate of 25 entities per hour and an idling ratioof 4% Define the system’s birth rate. Define at least two ways of arriving at the number of entities in the system. Define the ratio of the time an entity spends waiting and the time the entity spends in thesystem?
A grocery is supplied from 3 suppliers Fi(i = 1,2,3) who have: F1 of 5 trucks, F2 of 4 trucks and F3 of 6 trucks. The grocery is planned for a period of time, 12 trucks of goods. The transport from each supplier costs 40 monetary unitsfor F1, 60 monetary units for F2, respectively 50 monetary units for F3. Establish a supply schedule from the three suppliers so that the total cost of transport is as low as possible(minim cost). Observation: This is a linear program problem, i need only the mathematical model without solutions for the system, i only need those inequations.
The Pretty Cat Company wishes to introduce a new brand of cat dry foods that meets certain nutritional requirements. The biscuit-1 contains 2 units of nutrient A and 4 units of nutrient B, while biscuit-2 contains 2 units of nutrient A and 2 units of nutrient B. According to federal requirements, there must be at least 80 units of nutrient A and 120 units of nutrient B in a package of the new dry food (biscuit mix). In addition, the company has decided that there can be no more than 30 biscuit-1 in a package. If it costs 2 cents to make a biscuit-1 and 4 cents to make a biscuit-2, what is the optimal product mix for a package of the new dry food in order to minimize the firm's cost? (a) Formulate this as a linear programming problem. (b) Find the optimal solution for this problem graphically. What is the total cost of a package of the new dry food using the optimal mix?
A private investment club has $200,000 earmarked for investment in stocks. To arrive at anacceptable overall level of risk, the stocks that management is considering have been classifiedinto three categories: high risk, medium risk, and low risk. Management estimates that high-riskstocks will have a rate of return of 15%/year; medium-risk stocks, 10%/year; and low-risk stocks,6%/year. The members have decided that the investment in low-risk stocks should be equal tothe sum of the investments in the stocks of the other two categories. Determine how much theclub should invest in each type of stock if the investment goal is to have a return of$20,000/year on the total investment. (Assume that all the money available for investment isinvested.)Note: Develop the linear system of equations from the above theory and solve the system byGauss Jordon Method.
Cecille Paper Company uses softwood and hardwood pulp as basic materials for producing converter-grade paper. Hardwood is 80% pulp fiber and 20% pulp binder, while softwood is 50% pulp fiber and 50% pulp binder. The cost per pound for hardwood and softwood is $.50 and $.40, respectively. The company s quality control expert specifies that in order for the product to meet quality standards, each batch must contain at least 12,000 pounds of pulp fiber and at least 6,000 pounds of pulp binder. Because of equipment limitations, the size of a batch cannot exceed 24,000 pounds. The Production Department recently received a new standard from the Cost Department, allowing $8,200 per batch. The production manager feels that this amount is too low, because such costs have never been less than $8,400. Required: Using the graphic method, determine the hardwood and softwood mix necessary to minimize the cost per batch.
Determine the equilibrium prices of three interdependent commodities that satisfyP1 + 3P2 + 3P3 = 32P1 + 4P2 + 3P3 = 37P1 + 3P2 + 4P3 = 35
A pharmacist wants to establish an optimal inventory policy for a new antibiotic that requires refrigeration in storage. The pharmacist expects to sell 2400 packages of this antibiotic at a steady rate during the next year. She plans to place several orders of the same size spaced equally throughout the year. The ordering cost for each delivery is $12, and carrying costs, based on the average number of packages in inventory, amount to $4 per year for one package. Use this information to answer the following questions. a) Let x be the order quantity and r the number of orders placed during the year. Find the inventory cost (ordering cost plus carrying cost) in terms of x and r. b) Find the constraint function. c) Determine the economic order quantity that minimizes the inventory cost and then find the minimum inventory cost. X=__________ C=$___________
Gulf Coast Electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. For the past several years, Gulf Coast Electronics has relied on two suppliers for its reservoir capacitors: Able Controls and Lyshenko Industries. A new firm, Boston Components, inquired into the possibility of providing a portion of the reservoir capacitors needed by Gulf Coast. The quality of products provided by Lyshenko Industries has been extremely high; in fact, only 0.5% of the capacitors provided by Lyshenko had to be discarded because of quality problems. Able Controls has also had a high quality level historically, producing an average of only 1% unacceptable capacitors. Because Gulf Coast Electronics has had no experience with Boston Components, it estimated Boston’s defective rate to be 10%. Gulf Coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 75,000 acceptable-quality capacitors to use…
A can of cat food, guaranteed by the manufacturer to contain at least 10 units of protein, 20units of mineral matter, and 6 units of fat, consists of a mixture of four different ingredients.Ingredient A contains 10 units of protein, 2 units of mineral matter, and 1 2 unit of fat per100g. Ingredient B contains 1 unit of protein, 40 units of mineral matter, and 3 units of fat per100g. Ingredient C contains 1 unit of protein, 1 unit of mineral matter, and 6 units of fat per100g. Ingredient D contains 5 units of protein, 10 units of mineral matter, and 3 units of fatper 100g. The cost of each ingredient is 3c, 2c, 1c, and 4c per 100g, respectively. How manygrammes of each should be used to minimise the cost of the cat food, while still meeting theguaranteed composition?

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