Example 4-1. Suppose that a product is produced in three factories X, Y and Z. It isknown that factory X produces thrice as many items as factory Y, and that factories Y and Zproduce the same number of items: Assume that it is known that 3 per cent of the itemsproduced by each of the factories X and Z are defective while 5 per cent of those nanufacturedby factory Y are defective. All the itenis produced in the three factories are stocked, and an itemof product is selected at randoni.(i) What is the probability that this item is defective ?(ii) If an item selected at randoı is found to be defective, what is the probability that itwas produced by factory X, Y and Z respectively ?

Answered: Image /qna-images/answer/7c636846-feb8-4465-96b7-093ed897e6bc.jpg

Answered: Example 4-1. Suppose that a product is…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 24EQ: Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry...

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Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry requires $0.30 of coal and $0.70 of steel. Every $1 produced by steel requires $0.80 of coal and $0.20 of steel. Find the annual production (output) of coal and steel if the total annual production is $20 million.
Prove the half of Theorem 3.3 (e) that was not proved in the text.
that the amounts of time (in minutes) required for assembling the frames, installing the wheels, and decorating for the Starstreak and Superstreak models are as given in the following table: Frame Wheels Decoration Starstreak 25 6. 16 Superstreak 14 9 12 Assume also that each day the company has available 135 hours of labor for assembling frames, 95 hours of labor for installing wheels, and 110 hours of labor for decoration. Assume also that the profit on each Starstreak bike is $22.00 and the profit on each Superstreak bike is $26.00. How many bikes of each type should the company make in order maximize its profit?
Suppose a company manufactures different electronic components for a computer. Component A requires 2hours of fabrication and 1hour of assembly; Component B requires 3hours of fabrication and 1hour of assembly and component C requires 2hours of fabrication and 2hours of assembly. The company has up 1000 Labour hours for fabrication and 800 labour hours assembly each week. If proof on each component A,B, and C is K7,K8 and K10 respectively.How many of each should be produced to maximize?
3
2. A bank operates both a drive-up facility and a walk-up window. On a randomly selected day, let X = the proportion of time that the drive-up facility is in use (at least one customer is being served or waiting to be served) and Y = the proportion of the time that the walk-up window is in use. Then the set of possible values for (X, Y) is the rectangle D = {(x, y): 0 ≤ x ≤ 1,0 ≤ y ≤ 1}. Suppose the joint probability density function of (X, Y) is given by: fx,y(x,y) = { / (x + y ² ) ²²(x + y²) 0≤x≤ 1,0 ≤ y ≤ 1 Otherwise 0 (a) Show that fx,y is legitimate (b) Find the probability that neither facility is busy more than one-quarter of the time. (c) Find fx and fy, the marginal probability density function of X and Y respectively. (d) Construct the conditional probability density function of Y given that X=0.8. (e) Evaluate the probability that the walk-up facility is busy at most half of the time given that X=0.8 (f) Calculate the expected proportion of the time that the walk-up facility…
There are 2 countries, D and F. There are 2 products X and Y. Each country has only a single input labor hours, Li j, where i is D for Domestic or F for Foreign and j is either X for Good X use of the labor or Y for Good Y use of labor. In country D: In country F: Xp = an*LD, x - bo*LD, Y LD = LD, x + LD, Y XF = ag*LF, X YF = be*LF, Y LF = LF, X + LF, Y YD = At the moment: ap = 0.25, bp = 0.5, LD = 32, aE = 0.8, br = 0.4, LF = 40. Each country is operating in autarky and has determined to divide its labor force equal between the production of X and Y. In Autarky find complete the following tables: 1. Find hours (amount of L;) in each country to produce 1 unit of each good. Hours to 1 unit Y F 2. In D, what is the cost of 1 unit of X? X= Y 3. In D, what is the cost ofl unit of Y? Y = 4. In F, what is the cost of 1 unit of X? X = Y 5. In F, what is the cost of 1 unit of Y? Y =
Can you please include where the Gross Req (week) and Order Release (week), where the need to go on here?
4. A car traveling along a street needs to pass through 4 intersections with traffic lights. If each signal lamp displays the red and green signals at the same time, and each signal lamp works independently of each other. The number of intersections that the car has passed before encountering the red light for the first time is represented by X. Find the pmf of X.
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6. A population of fish is living in an environment with limited resources. This environment can only support the population if it contains no more than M fish (otherwise some fish would starve due to an inadequate supply of food, etc.). There is considerable evidence to support the theory that, for sorne fish species, there is a minimmum population m such that the species will bexzome extinet if the size of the population falls below m. Such a populalion can be modelled using a modilied logistic equatioa: dP dt (a) Use the differential equation to show that any solution is increasing if m < P< M and decreasing if 0 < P

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