Question

5. Eastern Engineering Company is trying to decide which of 6 projects to perform during the next quarter. The net present value, the estimated cost, and the number of engineers and staff personnel required for each project are given in the following table.

Project	Net Present Value ($1000’s)	Cost ($1000’s)	Engineers Required	Staff Required
1	100	35	5	2
2	145	65	8	3
3	200	95	11	2
4	250	180	4	2
5	500	250	16	7
6	695	475	19	11

Eastern has a $550,000 budget and 30 engineers and 15 staff available. Which projects should Eastern perform during the quarter?

Answer 1

The project table is:

Project	Net Present Value ($1000s)	Cost ($1000s)	Engineers Required	Staff Required
1	100	35	5	2
2	145	65	8	3
3	200	95	11	2
4	250	180	4	2
5	500	250	16	7
6	695	475	19	11

Budget available = $550,000 = $550*1000

Engineers available = 30

Staff Available = 15

We have to find the projects should be performed.

We have to select the projects such as to maximize the Net Present Value.

Let Project 1 = x1

Project 2 = x2

Project 3 = x3

Project 4 = x4

Project 5 = x5

Project 6 = x6

If value of xi = 1, then the project will be chosen

If value of xi = 0, then the project wont be chosen

Objective:

We have to maximize the Net Present Value.

Maximize 100*x1 + 145*x2 + 200*x3 + 250*x4 + 500*x5 + 695*x6

Constraints:

The total cost used should not exceed the budget.

35*x1 + 65*x2 + 95*x3 + 180*x4 + 250*x5 + 475*x6 <= 550

Total engineers used should not exceed engineers available. Total staff used should not exceed the total staff available.

5*x1 + 8*x2 + 11*x3 + 4*x4 + 16*x5 + 19*x6 <=30 (for engineers)

2*x1 + 3*x2 + 2*x3 + 2*x4 + 7*x5 + 11*x6 <= 15 (for staff)

The project can be either be selected or rejected. Hence another constraint is the decision variables being binary.

x1:x6 : binary

Putting everything in excel:

Solver Parameters:

Optimal Solution:

Hence,

The projects that Eastern should perform during the quarter: Project 2, Project 4 and Project 5

The Net Present Value is: $895000

The total cost of all the projects is: $495000

Engineers Used: 28

Staffs Used: 12

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