Question

Consider a capital budgeting problem with six projects represented by 0-1 text{variables} x1, x2, x3, x4, x5, text{and} x6. a. Write a constraint mode

Modeling
ANSWERED
asked 2021-03-02

Consider a capital budgeting problem with six projects represented by \(0-1\ \text{variables}\ x_1,\ x_2,\ x_3,\ x_4,\ x_5,\ \text{and}\ x_6.\)
a. Write a constraint modeling a situation in which two of the projects 1, 3, and 6 must be undertaken.
b. In which situation the constraint "\(x_3\ -\ x_5 = 0\)" is used, explain clearly:
c. Write a constraint modeling a situation in which roject 2 or 4 must be undertaken, but not both.
d. Write constraints modeling a situation where project 1 cannot be undertaken IF projects 3. also is NOT undertaken.
e. Explain clearly the situation in which the following 3 constraints are used simulataneously (together):
\(\displaystyle{x}_{4}\le{x}_{1}\)
\(\displaystyle{x}_{4}\le{x}_{3}\)
\(\displaystyle{x}_{4}\ge{x}_{1}+{x}_{3}-{1}\)

Expert Answers (1)

2021-03-03

Since you have posted multiple sub parts questions but according to guidelines, we will solve first three sub parts for you. For rest of the sub parts resubmit the question again and specify the part you want us to solve.
Consider a capital budgeting problem with 6 projects represented by 0 or 1 and variables \(\displaystyle{x}_{{1}},{x}_{{2}},{x}_{{3}},{x}_{{4}},{x}_{{5}},{x}_{{6}}.\)
For part (a) it is required to find the constraint modelling a situation in which two of the project 1,3 and 6 must be undertaken.
\(\displaystyle{x}_{{1}}+{x}_{{3}}+{x}_{{6}}\ge{2}\) For part (b) it is required to find the situation of the constraint \(\displaystyle{x}_{{3}}-{x}_{{5}}={0}.\)
constraint: \(\displaystyle{x}_{{3}}-{x}_{{5}}={0}\)
Project 3 and 5 must be selected together and none of them cannot be selected alone
\(\displaystyle\text{so}\ <\ {\left({x}_{{3}},{x}_{{5}}\right)}={\left({1},{1}\right)}{\quad\text{or}\quad}{\left({0},{0}\right)}\)
\(\displaystyle\Rightarrow{x}_{{3}}-{x}_{{5}}={0}\)
For part (c) it is required to write a constraint modelling a situation in which project 2 or 4 must be taken but not both.
\(\displaystyle{x}_{{2}}+{x}_{{4}}={1}\)
From the above constraint it is assure that one of the project is taken at a time not both as either
\(0\ +\ 1 = 1\ \text{or}\ 1\ +\ 0 = 1\)

12
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-03-02

Let \(x_1 = 94,210, x_2 = 8631, x_3 = 1440, x_4 = 133,\) and \(x5 = 34.\) Calculate each of the following, using four-digit decimal floating-point arithmetic: \(x1 + ((x2 + x3) + (x4 + x5))\)

asked 2021-02-25
We will now add support for register-memory ALU operations to the classic five-stage RISC pipeline. To offset this increase in complexity, all memory addressing will be restricted to register indirect (i.e., all addresses are simply a value held in a register; no offset or displacement may be added to the register value). For example, the register-memory instruction add x4, x5, (x1) means add the contents of register x5 to the contents of the memory location with address equal to the value in register x1 and put the sum in register x4. Register-register ALU operations are unchanged. The following items apply to the integer RISC pipeline:
a. List a rearranged order of the five traditional stages of the RISC pipeline that will support register-memory operations implemented exclusively by register indirect addressing.
b. Describe what new forwarding paths are needed for the rearranged pipeline by stating the source, destination, and information transferred on each needed new path.
c. For the reordered stages of the RISC pipeline, what new data hazards are created by this addressing mode? Give an instruction sequence illustrating each new hazard.
d. List all of the ways that the RISC pipeline with register-memory ALU operations can have a different instruction count for a given program than the original RISC pipeline. Give a pair of specific instruction sequences, one for the original pipeline and one for the rearranged pipeline, to illustrate each way.
Hint for (d): Give a pair of instruction sequences where the RISC pipeline has “more” instructions than the reg-mem architecture. Also give a pair of instruction sequences where the RISC pipeline has “fewer” instructions than the reg-mem architecture.
asked 2021-05-23
The reduced row echelon form of a system of linear equations is given.Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1,x2,x3,x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution.
asked 2021-05-05
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y;x,y; or x,y,z;x,y,z; or x1,x2,x3,x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. [1001−40][
...