Question

In: Statistics and Probability

Project Selection Your company is prepared to undertake several new projects over the next five years....

Project Selection

Your company is prepared to undertake several new projects over the next five years. Each Division has submitted a number of project proposals that include the annual budgets and anticipated profit. Your company’s annual budgets for the next five years are as follows. (Amounts are X$1000)

YEAR	2016	2017	2018	2019	2020
FUNDS	3500	4500	4000	3450	4500

The project proposals (for a total of fifteen possible projects) are as follows:

Project	2016	2017	2018	2019	2020	Profit
1	400	230	330	400	230	1500
2	500	270	260	500	270	2000
3	200	430	430	200	430	2500
4	300	220	270	300	220	7000
5	450	500	400	450	500	4000
6	650	450	320	650	450	3000
7	350	530	330	350	530	4500
8	300	700	260	300	700	3500
9	500	800	430	500	800	1500
10	600	250	270	600	250	2000
11	150	500	400	150	500	2500
12	250	340	320	250	340	7000
13	220	400	250	220	270	4000
14	170	300	300	170	300	3000
15	420	400	260	420	400	4500

What project selection should your company choose? (You decide what criterion to use, but recall that this Business school.)

Please show/explain using excel solver

Solutions

Expert Solution

Answer: Projects Chosen: 3,4,5,6,7,8,12,13,14,15

Profit : 43000

Step 1: Decision Variables of the Problem are as follows-

Here, we have 15 decision Variables i.e Projects chosen. Let's say Projects to be X1, X2,.......X15

Step 2: Objective Function: Maximize Profit by the selection of the projects.

1500*X1+2000*X2+2500*X3+7000*X4+4000*X5+3000*X6+4500*X7+3500*X8+1500*X9+2000*X10+2500*X11+7000*X12+4000*X13+3000*X14+4500*X15

Step 3: Constraints:

for 2016:

1) 400*X1+500*X2+200*X3+300*X4+450*X5+650*X6+350*X7+300*X8+500*X9+600*X10+150*X11+250*X12+220*X13+170*X14+420*X15 <= 3500

2) for 2017

230*X1+270*X2+430*X3+220*X4+500*X5+450*X6+530*X7+700*X8+800*X9+250*X10+500*X11+340*X12+400*X13+300*X14+400*X15<= 4500

3) for 2018

330*X1260*X2+430*X3+270*X4+400*X5+320*X6+330*X7+260*X8+430*X9+270*X10+400*X11+320*X12+250*X13+300*X14+260*X15<=4000

4) for 2019

400*X1+500*X2+200*X3+300*X4+450*X5+650*X6+350*X7+300*X8+500*X9+600*X10+150*X11+250*X12+220*X13+170*X14+420*X15 <=3450

5) for 2020

230*X1+270*X2+430*X3+220*X4+500*X5+450*X6+530*X7+700*X8+800*X9+250*X10+500*X11+340*X12+270*X13+300*X14+400*X15 <=4500

6)Xi = binary, i=1,2,3,.......15

Below, I have attached the solved excel worksheet in the solver

The decision should be made in order to maximize the profit by the undertaken projects and funds needed by the chosen projects need to be within funds available to the company.

Thank You!

orchestra answered 1 year ago

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