Only hand written otherwise skip... We assume that in a village there are farmers, carpenters, and tailors, who provide the three essential goods: food, housing, and clothing. Suppose thefarmers consume of the food (produced by farmers), of the housing (produced by carpenters) and of the clothes (produced by tailors). Thecarpenter consumes of the food. of the housing, and of the clothes. The tailors consume of the food, of the housing, and no clothes.Assume this is a closed Leontief modelIf we know that the tailors produce 280 units of clothes, then the farmers producehousingunits of food and the carpenters produceunits of

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Answered: We assume that in a village there 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 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...

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1. Suppose that, in Example 2.27, 400 units of food A, 600 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 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2
Suppose each of three construction industries—dwellings construction, roads and bridges construction, and public and private businesses construction—requires the following input in order to produce one dollar in output. The dwellings construction industry requires nothing from itself, 3/10 of a dollar from roads and bridges construction, and 1/4 of a dollar from public and private businesses construction. The roads and bridges construction industry requires 3/8 of a dollar from dwellings construction, none from itself, and 2/5 of a dollar from public and private businesses construction. The public and private businesses construction industry requires 1/10 of a dollar from dwellings construction, 1/6 of a dollar from roads and bridges construction, and none from itself. Suppose further that the total production capacity of the dwellings construction industry is $360, of roads and bridges construction is $480, and of public and private businesses construction is $420. Find the…
There are two types of female honeybees: workers, which produce no eggs, and the queen, which produces eggs. Drone bees are males that are produced from the queen’s unfertilized eggs. A drone’s mother is the queen that laid the egg. But a drone has no father, because the egg was never fertilized. Worker females and queen females are produced from the queen’s fertilized eggs. So each type of female has a father as well as a mother, because the female eggs were fertilized. Describe how the numbers of ancestors of a drone honeybee are Fibonacci numbers.
A greeting card manufacturer has 500 boxes of a particular card in warehouse I and 290 boxes of the samecard in warehouse II. A greeting card shop in San Jose orders 350 boxes of the card, and another shop inMemphis orders 250 boxes. The shipping costs per box to these shops from the two warehouses areshown in the following table:DESTINATIONSan Jose MemphisWarehouse I $0.25 $0.22Warehouse II $0.23 $0.21How many boxes should be shipped to each city from each warehouse to minimize shipping costs? Do notsolve; however, set up the constraints and the objective function. Describe all variables that are used inthe constraints.
A company wishes to produce three types of souvenirs: types A, B, and C .To manufacturers a type- A souvenir requires 2 minutes on machine I, 1 minute on machine II, and 2 minutes on machine III. A type- B souvenir requires 1 minute on machine I, 3 minutes on machine II, and 1 minute on machine III. A type-C souvenir require 1 minutes on machine I and 2 minute each one machine II and III. There are 3 hours available on machine I, 5 hours available on machine II, and 4 hours available on machine III, for processing the order. How many souvenirs of each type should be the company make in order to use all the available time.

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