Question

In: Statistics and Probability

The Charming City Construction Company is considering six projects. The projects, the number of supervisors and...

The Charming City Construction Company is considering six projects. The projects, the number of supervisors and the number of workers required for each project, and the expected profits for each project are given below.

Project

1 2 3 4 5 6

________________________________________________________________

Supervisors Required 5 4 6 3 4 2

Workers Required 15 24 35 22 26 32

Profit (in thousands of dollars) 210 290 330 240 300 200

The objective is to maximize the company's total expected profit subject to the following constraints:

- Use no more than 20 supervisors

- Use no more than 108 workers

- If project 4 is done, then project 2 must be done and vice versa

- At least four projects are to be done.

Formulate a capital budgeting integer optimization problem by defining

(a) The decision variables

(b) The objective function. What does it represent?

(c) All the constraints. What does each constraint represent?

Solutions

Expert Solution

Answer:

We will formulate this problem as below:

(a) Decision variables

Xi= 1 if a project i is selected else 0 (binary variable)

X1= 1 if a project 1 is selected else 0

X2= 1 if a project 2 is selected else 0

X3= 1 if a project 3 is selected else 0

X4= 1 if a project 4 is selected else 0

X5= 1 if a project 5 is selected else 0

X6= 1 if a project 6 is selected else 0

(b) Objective function

The objective is to maximize total expected profit from the projects. Total profit will be sum of the product of expected profit from projects and variable to select the project.

MAX z= 210X1+290X2+330X3+240X4+300X5+200X6

(c)

Constraints:

5X1+4X1+6X3+3X4+4X5+2X6 <= 20

(this represents use no more than 20 supervisors)

15X1+24X2+35X3+22X4+26X5+32X6 <= 108

( this represents use no more than 108 workers)

X2=X4

(this represents if project 4 is done, then project 2 must be done and vice versa)

X1+X2+X3+X4+X5+X6 >= 4

(this represents at least four projects are to be done)

X1, X2, X3, X4, X5, X6= {0,1}; all Xi's are binary variable

Please give thumbs up/ like if you find this answer helpful. Thank you!


Related Solutions

6. The Charming City Construction Company is considering six projects. The projects, the number of supervisors...
6. The Charming City Construction Company is considering six projects. The projects, the number of supervisors and the number of workers required for each project, and the expected profits for each project are given below.                                                                                       Project                                                                  1           2           3           4           5           6            ________________________________________________________________             Supervisors Required                 5            4           6           3           4           2           Workers Required                      15          24         35         22        26         32           Profit (in thousands of dollars) 210        290       330       240      300      200...
6. The Charming City Construction Company is considering six projects. The projects, the number of supervisors...
6. The Charming City Construction Company is considering six projects. The projects, the number of supervisors and the number of workers required for each project, and the expected profits for each project are given below.                                                                                       Project                                                                  1           2           3           4           5           6            ________________________________________________________________             Supervisors Required                 5            4           6           3           4           2           Workers Required                      15          24         35         22        26         32           Profit (in thousands of dollars) 210        290       330       240      300      200...
The City of Waterman established a capital projects fund for the construction of an access ramp...
The City of Waterman established a capital projects fund for the construction of an access ramp from the parking garage to the city’s office building to be used by individuals with disabilities. The estimated cost of the ramp is $217,000. On January 1, 20X2, a 10 percent, $154,000 bond issue was sold at 103 with the premium transferred to the debt service fund. At that date, the county board provided a $63,000 grant. After a period of negotiation, the city...
The City of Waterman established a capital projects fund for the construction of an access ramp...
The City of Waterman established a capital projects fund for the construction of an access ramp from the parking garage to the city’s office building to be used by individuals with disabilities. The estimated cost of the ramp is $200,000. On January 1, 20X2, a 10 percent, $150,000 bond issue was sold at 104.0 with the premium transferred to the debt service fund. At that date, the county board provided a $50,000 grant. After a period of negotiation, the city...
Diamond City is considering two mutually exclusive investment projects. The cost of capital for these projects...
Diamond City is considering two mutually exclusive investment projects. The cost of capital for these projects is r. The projects’ expected net cash flows are as follows: Year Project A Project B 0 -42,000 -42,000 1 24,000 16,000 2 20,000 18,000 3 16,000 22,000 4 12,000 26,000 a. If r = 10%, which project should be selected under the NPV method? b. If r = 20%, which project should be selected under the NPV method? c. Calculate each project’s PI...
Diamond City is considering two mutually exclusive investment projects. The cost of capital for these projects...
Diamond City is considering two mutually exclusive investment projects. The cost of capital for these projects is r. The projects’ expected net cash flows are as follows: Year Project A Project B 0 -42,000 -42,000 1 24,000 16,000 2 20,000 18,000 3 16,000 22,000 4 12,000 26,000 a. Calculate each project’s payback (PB) period if r = 10% (up to 2 decimal places). Which project should be accepted? b. Calculate each project’s discounted payback (DPB) period if r = 10%...
Doug’s Custom Construction Company is considering three new projects, each requiring an equipment investment of $...
Doug’s Custom Construction Company is considering three new projects, each requiring an equipment investment of $ 24,640. Each project will last for 3 years and produce the following net annual cash flows. Year AA BB CC 1 $ 7,840 $ 11,200 $ 14,560 2 10,080 11,200 13,440 3 13,440 11,200 12,320 Total $ 31,360 $ 33,600 $ 40,320 The equipment’s salvage value is zero, and Doug uses straight-line depreciation. Doug will not accept any project with a cash payback period...
A city is considering buying a piece of land for $500.000 and construction an office complex...
A city is considering buying a piece of land for $500.000 and construction an office complex on it. Their planning horizon is 20 years. Two mutually exclusive building designs have been drawn up by an architectural firm. Use the modified benefit cost ratio method and a MARR of 10% per year to determine which alternative should be recommended to the city council. Design A (x1000$) Design B (x1000$) Cost of building including cost of the land 1,048 1,315 Resale value...
A city is considering buying a piece of land for $500.000 and construction an office complex...
A city is considering buying a piece of land for $500.000 and construction an office complex on it. Their planning horizon is 20 years. Two mutually exclusive building designs have been drawn up by an architectural firm. Use the modified benefit cost ratio method and a MARR of 10% per year to determine which alternative should be recommended to the city council. Design A (x1000$) Design B (x1000$) Cost of building including cost of the land 1,107 1,306 Resale value...
A city is considering buying a piece of land for $500.000 and construction an office complex...
A city is considering buying a piece of land for $500.000 and construction an office complex on it. Their planning horizon is 20 years. Two mutually exclusive building designs have been drawn up by an architectural firm. Use the modified benefit cost ratio method and a MARR of 10% per year to determine which alternative should be recommended to the city council. Design A (x1000$) Design B (x1000$) Cost of building including cost of the land 1,192 1,320 Resale value...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT