The Charm City Construction Company is considering six projects. The projects, t
ID: 454625 • Letter: T
Question
The Charm 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
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Supervisors Required 4 3 5 3 4 2
Workers Required 15 24 35 20 24 30
Profit (in thousands of dollars) 200 280 320 220 280 180
The objective is to maximize the company's total expected profit subject to the following constraints:
- Use no more than 15 supervisors
- Use no more than 100 workers
- If project 2 is done, then project 4 must be done and vice versa
- At least four projects are to be done.
Formulate a capital budgeting integer programming problem by defining
(a) The decision variables.
(b) The objective function. What does it represent?
(c) All the constraints. What does each constraint represent?
Explanation / Answer
Let X1 , X2 , ...X6 be the 6 projects also these variables have 0-1 values indicating whether projects are not done or are done.
Then we have the objective function as
Maximize, Z= 200*X1 +280*X2 + 320*X3 + 220*X4 + 280*X5 +180*X6
subject to the constraints
4*X1 + 3*X2 + 5*X3 + 3*X4 + 4*X5 + 2*X6 <=15
15*X1 +24*X2 + 35*X3 + 20*X4 + 24*X5 + 30*X6 <=100
X2 - X4 >= 0
X1 + X2 + X3 + X4 + X5 + X6 >= 2
X1 , X2 , ...X6 >= 0