# (Solved Homework): EMGT 609-45 Engineering Cost Analysis Homework # 8 Due Date: 6:00 PM, Tuesday…

EMGT 609-45 Engineering Cost Analysis Homework # 8 Due Date: 6:00 PM, Tuesday, September 12 Problem 1 (chapter 13) Three alternatives are being considered for an engineering project. Their cash -flow estimates are shown in the accompanying table. A and B are mutually exclusive, and C is an optional add-on feature to alternative A. Investment funds are limited to \$6,000,000. Another constraint on this project is the engineering personnel needed to design and implement the solution. No more than 12,000 person-hours of engineering time can be committed to the project. MAR-10%. Initial investment (\$106) After-tax annual savings (\$106), years one through five 1.3 2.20.9 Personnel requirement (hours) 4.0 4.5 1.0 7,000 9,000 3,000 1) Set up a linear integer programming formulation of this resource allocation problem 2) Use Excel solver to find the optimal solutions. Submit your spreadsheet solutions only) 3) Interpret your results. Problem 2 (chapter 14) See attached Excel file to find the table of alternatives and attributes. The weights are defined by you (i.e. you can assign a higher weight value for the attribute which are more important to you) Using the Additive Weights Method, rank the alternatives and determine which the superior alternative is? (Submit your spreadsheet solutions only)

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First, we will find Present Values (PV) of each of the A, B, and C.

 Year Cash Flows Discount factor A B C 0 (\$4.00) (\$4.50) (\$1.00) 1.000 1 \$1.30 \$2.20 \$0.90 0.909 2 \$1.30 \$2.20 \$0.90 0.826 3 \$1.30 \$2.20 \$0.90 0.751 4 \$1.30 \$2.20 \$0.90 0.683 5 \$1.30 \$2.20 \$0.90 0.621 PV \$0.928 \$3.840 \$2.412

Formulation

Let YA, YB, and YC are the binary integer representing the selection of A, B, and C respectively such that Yi = 1 when project ‘i’ is selected and equal to 0 otherwise. ∀i = {A, B, C}

Objective Function – max.Z = Total Present Value = 0.928YA + 3.84YB + 2.412YC

Subject to,

Limited budget: 4YA + 4.5YB + 1YC ≤ 6

A and B are mutually exclusive: YA + YB ≤ 1

C is an add-on to A: YC – YA ≤ 0

Limited person-hours: 7YA + 9YB + 3YC ≤ 12

Excel Setup

So, as per the results, selecting project B is most beneficial.

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