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.
The Ace Manufacturing Company has orders for three similar products. Orders (units) 2,200 Product A B C с 1 2 Machine 3 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A A B B C с Product 1 2 3 300 1,400 Capacity (units) 1,800 1,700 800 1 Machine 2 3 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20
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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 =
Suppose a maquiladora with two types of parts as raw material: type A and type B. In a first stage of assembly using A and Bs the weapon types are produced two M and N. In a second stage of assembly using the types M and N the types of reinforcements X and Y are produced. knows that to assemble 4 Xs and 3 Ys, a total of 38 Ms and 20 Ns and that to assemble 4 Xs and 1 Ys were required in total 26 Ms and 12 Ns. Furthermore, it is known that to obtain an M requires 4 As and 4 Bs and for an N requires 1 As and 2 Bs. Indicate, in order, how many A and B pieces required to build an X and how many to build a Y. Determine: A) the system of linear equations that models the previous context. B) the solution of the system using some SEL solution method seen in class (example: Gaussian elimination; Gauss-Jordan; Cramer's rule, etc.). C) Respond to the problem raised.
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 demand for subassembly S is 100 units in week 7. Each unit of S requires 1 unit of T and 2 units of U. Each unit of T requires 2 units of V, 1 unit of W, and 1 unit of X. Finally, each unit of U requires 1 unit of Y and 3 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, 1 week to make V, 3 weeks to make W, 1 week to make X, 2 weeks to make Y, and 1 week to make Z. a) Choose the correct product structure. ○ A. Level 0 S 1 ○ C. U(2) 2 T (1) W (1) X(1) Y(1) Z(3) Level 0 S 1 T(1) 2 V(2) Y(1) Z (3) W (1) X (1) ☑ B. Level 0 S T(1) U(2) 1 2 V(2) W (1) X(1) Y(1) Z(3) → Level 0 S V(2) ☑ b) Choose the correct time-phased product structure. ○ A. B. Z V U Y W T ☑ Π ☑ S T W Y U Z ○ C. 1 2 Y(1) W (1) X (1) U(2) Z(3) V W T ☑ S Y U Z ☑ ☑ ○ D. W T ☑ S Y U Z 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 7 1 2 3 4 5 6 7 Time in weeks Time in weeks Time in weeks Time in weeks ☑
A company produces three products P, Q and R using raw materials A, B and C. One unit of P requires 1, 2 and 3 units of A, B and C respectively. One unit of Q requires 2, 3 and 2 units of A, B and C respectively. One unit of R requires 1, 2 and 2 units of A, B and C respectively. The number of units available for raw material A, B and C are 8, 14 and 13 units respectively. Using the matrix method, determine the number of units of each product to produce in order to utilize completely the available resources
The demand for subassembly S is 120 units in week 7. Each unit of S requires 1 unit of T and 2 units of U. Each unit of T requires 2 units of V, 1 unit of W, and 1 unit of X. Finally, each unit of U requires 1 unit of Y and 3 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, 1 week to make V, 3 weeks to make W, 2 weeks to make X, 2 weeks to make Y, and 2 weeks to make Z. Click the icon to view the product structure and the time-phased product structure. Construct a gross material requirements plan (type 0 if the input box is not used). Item 1 2 3 Week 4 Lead Time 5 6 7 (weeks) S Gross req Order release 2 T Gross req Order release 1 U Gross req Order release 2 V Gross req Order release 1 W Gross req Order release 3 Gross req Order release 2 Y Gross req Z On-Hand Inventory Item On-Hand Inventory ITIT Order release Gross req Order release 2 2

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