Question 1113555: Which of the following is a linear constraint?
5y + 3x2 ≥ 33
17x + 3xz ≤ 4
7x ≤ 3xy + 14z - 12
3x ≥ 14y + 2z + 13 Found 2 solutions by greenestamps, solver91311:Answer by greenestamps(13200) (Show Source):
"Linear" means each variable appears by itself, and only to the first power. Stated differently, each term is either a constant (no variables) or contains a single variable to the first power.
5y + 3x2 ≥ 33 no; can't have an x^2 term
17x + 3xz ≤ 4 no; can't have a term with the product of two variables
7x ≤ 3xy + 14z - 12 ditto
3x ≥ 14y + 2z + 13 yes!
In order to be a linear constraint, all of the terms must be linear or constant. A linear term is one where the sum of the exponents on the variables in the term is 1 and a constant term is where the sum of the exponents on the variables is 0. If a term has no visible variables, you can assume as many variables as you like are there so long as all of the exponents are zero. If you see a variable without an exponent, you can assume an exponent of 1 on that variable. Symbolically: no matter what is. And
Examples:
A constant term, aka a term of degree 0:
A linear term, aka a term of degree 1. Note the sum of the exponents is 1:
A non-linear term, in this case a term of degree 2. Note the sum of the exponents is 2:
John
My calculator said it, I believe it, that settles it
