I have a very simple linear problem: <mtable columnalign="right left" rowspacing="3pt" column

Brenden Tran 2022-06-23 Answered
I have a very simple linear problem:
min x   x 2 s.t.    a 1 x 1 + a 2 x 2 = b
Suppose I want to write this problem equivalently as in Find the equivalent linear program. Unlike the problem in the link, I have equality. Can I write it equivalently as:
min x , α , β   x 2 s.t.    a 1 x 1 = α b ,   a 2 x 2 = β b ,   α + β = 1.
The converse is intuitive: Given { x , α , β } feasible for the second problem, adding the first and second constraints gives the constraint of the first problem. But the forward part is not clear, especially because I have never seen an equality constraint written like this. Any help would be highly appreciated.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

EreneDreaceaw
Answered 2022-06-24 Author has 20 answers
You are correct. Suppose x is feasible. Then a 1 x 1 + a 2 x 2 = b ( a 1 x 1 + a 2 x 2 = ( α + β ) b  and  α + β = 1 ) . Therefore any solution satisfying the latter conditions is also feasible.

A simple example to explain what I think is the part you are unclear about is the following. Look at the following two problems:
1.
min x   x s.t.    x 2 x R
2.
min x   x s.t.    x 2 x 1 x R
They obviously generate the same feasible solution; the constraint added is weaker than the existing constraint. Similarly the following problem also generates the same feasible solution:
min x , a   x s.t.    x a a = 2 x R
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-02-25
Evaluate Cx2y2dx+4xy3dy where C is the triangle with vertices(0,0),(1,3), and (0,3).
(a)Use the Greens
asked 2020-12-29
Use the Divergence Theorem to find the flux of F=xy2i+x2yj+yk outward through the surface of the region enclosed by the cylinder x2+y2=1 and the planes z = 1 and z =-1.
asked 2021-09-22
Evaluate the definite integrals.Requires a supporting analysis.
095x
asked 2021-09-03
Sports salaries. Table shows the average salaries for players in Major League Baseball (MLB) and the National Basketball Association (NBA) in selected years since 1990.
a. Let x represent the number of years since 1990 and find exponential regression model y = abx for the average salary in MLB. Use the model to estimate the average salary (to the nearest thousand dollars) in 2022.
b. The average salary in MBL in 2000 was 1.984 million. How does this compare with the value given by the model of part (a)?
asked 2020-11-01
use Green’s Theorem to find the counterclockwise circulation and outward flux for the field F and the curve C. F=(y2x2)i+(x2+y2)j
C: The triangle bounded by y = 0, x = 3, and y = x
asked 2022-01-23
How do you find critical points for function of two variables f(x,y)=8x3+144xy+8y3?
asked 2021-09-04
Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
f(x)=x45x336x2+272x448
All complex zeros are=?