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 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

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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.
Consider a labor market for men and women with two types of workers in each group, high ability (H types), and low ability (L types). H types among men and women have a productivity of 70 and L types among men and women have a productivity of 30. Among women 2/3rds are H types, and 1/3rd are L types, and among men ½ are H types, and ½ L types. Suppose affirmative action for women reduces the cost of college for all women to 10. What happens to the average wage gaps between men and women? Recall that employers know the shares of H and L types, but cannot observe individual types. ● Women on average make around 12% more than men. ● Women on average will make 40% more than men. ● Men will make 40% more than women. ● Women on average make 2/3rds more than men.
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…
Can you please include where the Gross Req (week) and Order Release (week), where the need to go on here?
The demand for subassembly S is 130 units in week 7. Each unit of S requires 2 units of T and 1 unit of U. Each unit of T requires 2 units of V, 1 unit of W, and 2 units of X. Finally, each unit of U requires 2 units of Y and 2 units of Z. One firm manufactures all items. It takes 2 weeks to make S, 1 week to make T, 2 weeks to make U, 2 weeks to make V, 3 weeks to make W, 1 week to make X, 2 weeks to make Y, and 1 week to make Z. Click the icon to view the product structure and the time-phased product structure. Click the icon to view the on-hand inventory. Construct a net material requirements plan using on-hand inventory (enter your responses as whole numbers). The product structure. The time-phased product structure. Q Level V ° W T T(2) U(1) X 1 More Info Y U Z 2 V(2) W(1) X(2) Y(2) Z(2) 3 5 Time in weeks Week Item 1 2 3 4 5 6 7 S Gross req On hand Net req Order receipt Order release T Gross req U V W X Y On hand Net req Order receipt Order release Gross req On hand Net req Order…
The dependencies between the 10 activities listed in the table above are as follows:• The project starts with two activities—A, and B—which can be done concurrently.• When activity A is finished, activity C can start• When activity B is finished, activities D and E can start• When both activities C and D are finished, activity F can start• When activity E is finished, activity G can start• When activity F is finished, activity H can start• When both activities G and H are finished, activity I can start• When activity G is finished, activity J can start• The project is complete when activities I and J are finished Questions1. Organize the information above in an activity precedence table showing the activity, precedent and duration (calculated using the PERT weighted average formula and round to the nearest integer).2. Draw an AON network diagram and calculate its early start, early finish, late start and late finish times, floats (Free and total) for each activity. Make sure you…
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3 (1) dr.
1. Zombies have appeared in Chicago and every day, each zombie produces 3 new zombies. Suppose that initially there is only one zombie, how many zombies will there be in 7 days? 2. In a rabbit population, each pair produces 2.2 offspring every year (i.e. 1.1 per capita) and the adults have a 0.9 annual death rate after reproduction (and assume the whole population is paired up into mating pairs.) If initially there are 55 rabbits, predict how many there will be in 5 years (rounded to the nearest integer). 3. Consider the same rabbit population, but now a python that lives nearby eats exactly 1 rabbit a month. If initially there are 55 rabbits, how many do you predict will be in 10 years?
Suppose the entire cola industry produces only two colas. Given that a person last purchased cola 1, there a 70% chance that her next purchase will be cola 1. Given that a person last purchased cola 2, there is an 75% chance that her next purchase will be cola 2. Suppose that each customer makes one purchase of cola during any week (52 weeks=1 year). Suppose there are 150 million customers. One selling unit of cola costs the company $0.5 to produce and is sold for $2. For $200 million per year, Britney Spears (by an advertising song) guarantees to decrease from 30% to 15% the fraction of cola 1 customers who switch to cola 2 after a purchase. Should the company that makes cola 1 hire Britney Spears?

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