You are responsible for developing a supervisory training programme for a company. The following table shows the relationships between the activities that must be completed, along with estimates of the durations in days.

Table 1: Activity Times and Predecessors

Required
(a) Draw the activity network for this problem (either AON or AOA)
(b) Determine the Expected Time and Variance for each activity (show in a table).
Round off times to two decimal places where fractional.
(c) Show the activity schedule (ES, EF, LS, LF) as well as slack (in table).
(d) Determine and state the critical path for this project. This must be based on
your work in c) and not by inspection.
(e) What are the expected time and the variance of the project?
(f) What is the probability the project will be finished within 49 days?
(g) What time should be set such that there is a 99% chance of completion?
(h) What is the probability the project will take between 45 and 50 days?

MATH 383: WORKSHEET 9, WEDNESDAY APRIL 1Name:Problem 1.Write down the solution of the system of equationsc1−2c2+c3−c4=−2c2+ 2c3+ 2c4= 5c3+c4= 1c4=−1.What does the augmented coefficient matrix look like in this example?Problem 2.In this problem we will solve the system of equations−c1+c2+ 2c3−c4= 1c1+ 2c2−c3+ 0c4=−33c1−c2+c3+ 2c4= 80c1+c2+c3+c4= 2using elementary row operations.a) Write down the augmented coefficient matrix for this system of equations.

Using Matlab

1. Solve the following equations set

f1 (x1,x2) = sin (sin (x1)) +x2

f2 (x1,x2) = x1+ e^(x2)

a) Can this equation set be solved by the fixed - point method with the following expressions? And why? Show your analysis with a 2D graph.

g1 (x1,x2) = -e^(x2)

g2 (x1,x2) = -sin⁡(x1)

b) Use Newton Raphson Method with initial values x1 = -2, x2 = 1.5. (8 significant figures. Please submit the code and results.)

Geostatistics deviates from classic statistics in that Geostatistics is not tied to a population distribution model that assumes, for example, all samples of a population are normally distributed and independent from one another. Most of the earth science data (e.g., rock properties, contaminant concentrations) often do not satisfy these assumptions as they can be highly skewed and/or possess spatial correlation. a. Illustrate with the aid of diagram how and why any of such Earth Science data obtained from a given field would be skewed and possess spatial correlation. b. How would the spatial correlation property aid the Geostatistician in predicting the values of the unknown data points of a given field?

List the left and right cosets of H = {(1), (23)} in S3. Are they the same collection?

y''-2ay'+a^2y=60xe^{ax}+60x^2e^{ax}

Use the method of undetermined coefficients to find a particular solution for each equation. Then solve each equation for real general solution.

this is a non homogeneous differntial equation

1. Project flow and Report Format

The following information must be included in your report:

Abstract

Table of Content

List of Figures

List of Tables

LIST OF ABBREVIATIONS

Part 1: Introduction

Part 2: Literature Review

Part 3: Methodology

Part 4: Result and Discussion

Part 5: Conclusions

Part 6: References

Appendix

Initial Value Problem. Use Indeterminate Coefficients method for this problem:

y'' - 4y = sin(x)

where: y(0) = 4 and y'(0) = 8

On Matlab use BFGS Method to find the minimum of the following function: f(x) = x₁³ - 2x₂x₁² + x₁² - x₁using initial point (x₀, y₀) = (1, 2)^T to start, and stop when f changes less than 0.0001

2. (a) Solve the complex equation (1+?)?³−[1+?^?(?3)]=0 and list all possible solutions in Euler’s form with principal arguments.
(b) Express the complex number ?=(1−sin?+?cos?)²⁰ in Euler’s form.

You are the finance manager of your company. Your company is planning for capacity expansion and need to borrow RM850,000 from a local bank. The offered term loan will be amortised in 9 years with a nominal interest rate of 7.2% p.a. compounded monthly. The final payment will be at the end of Year 9.

1.Based on your working on an amortisation table, how much principal and interest would have your company paid after the first four months of payments?

2.If you have a choice, would you prefer to repay the above loan monthly (assume7.2% per year is compounded monthly) or annually (assume 7.2% per year is compounded annually) based on the total interest incurred? What is the main factor that contribute to such a difference in interest?

Let u = f(x,y), where x = rcosθ and y = rsinθ. Using the chain rules, carefully calculate the partial derivatives ∂u/ ∂r and ∂u/ ∂θ , and the second partial derivatives ∂2u/ ∂r2 and ∂2u/ ∂θ2 , in terms of r, θ, and the partial derivatives fx, fy, fxx, fxy, fyy.

∂u /∂r =

∂u /∂θ =

∂^2u/ ∂r^2 =

∂^2u ∂θ^2=

How many bit strings of length fifteen

a) Contain at least four 0s?

b) Contain at most four 0s?

c) Contain exactly four 0s?

d) Begin with four 0s?

Using Runge-Kutta method, compute y(0.3), from the equation dy dx = xy 1+x2 with y(0) = 1, take h = 0.1

If an undamped spring-mass system with a mass that weighs 6 lb and a spring constant 4 lbin is suddenly set in motion at t=0 by an external force of 63cos(12t) lb, determine the position of the mass at any time. Assume that g=32 fts2. Solve for u in feet.