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college maths

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Suppose that you have been asked to take over as a project manager on a small construction project which has been decomposed into 7 tasks – activities. Let Qi be the quantity of work for task i (expressed in labor days/machine days/ days needed to process the total amount of material per task), Li be the no. of labor required per task i, Mi be the amount of material required for task i, Ei be the no. of the construction equipment required for task i, Ti be the duration of task i in days. The given quantity of work is as follows:
Qi (for Mi) =12 in Task 1
Qi (for Li )= 20 in Task 2
Qi (for Ei) = 14 in Task 3
Qi (for Li) = 10 in Task 4
Qi (for Ei) = 9 in Task 5
Qi (for Mi ) = 12 in Task 6
Qi(for Ei) = 6 in Task 7

Task Li Ei Mi Ti
1 2 0 3
2 2 5 5
3 3 6 7
4 3 7 5
5 2 4 3
6 1 3 2
7 1 4 2

a) Determine manpower for tasks 2 and 4, materials for task 1 and 6, equipment requirements for tasks 3, 5 and 7 of a given construction situation. Calculate the total labor power and project duration.
b) Assume that the wage rate is £15/hr .Calculate the manpower cost for the initial project. If the project has to be completed in 20 days, you have to make a decision on increasing/decreasing a labor power. What is the suggested labor power in that case? Compare and contrast your solution to construction situation in terms of the total labor cost required for the initial project.
c) If an initial account of £47500 is invested for material payments in a construction project with 5% additional costs per day, how long should the project last before it triples its expenses?
d) Use the data on the no. of workers required (Li) and the quantity of work for task i (Qi) in order to prepare the appropriate graph. Fit straight line to the data using least squares method. Using the equation of the line of the best fit, estimate the value of Qi if Li is 5. What would be the duration (in days) of the task in that case?
e) Effective judgments have been made in relation to the choice of the total labor cost required for the project in Question b).
f) Check the validity of your estimated law in Question d) using the Pearson Correlation Coefficient.
g) Comment critically on how good you expect the forecast of Qi calculated in
Question d) to be.

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