## Linear Programming quiz questions

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
massmatics
Posts: 2
Joined: Mon Sep 14, 2015 9:26 am
Contact:

### Linear Programming quiz questions

I have some questions if my answers are correct and I just need anyone to verify and correct my solutions :(.

A.Given an optimal solution to an LP model, is there a case when the value of z is negative? Justify your answer.
My solution: Yes, the value of z can be negative if the gradients of X1 and X2 are negative.. (Is that correct?)

B. What is the effect of converting an LP model into its standard form to its number of constraints?
My solution: The main reason one is converting LP model into standard form is that this form is the starting point for the simplex method.
Also, it is to eliminate the consideration of minimization-type objectives..

C. How many additional slack variables will you have after converting an LP model to its standard form?
My solution: I said that the adding the slack variables depends on how many constraints which have a <= (less than or equal sign) there are. For example, if you have 2 constraints with <=, then you will have to add 2 slack variables..

D.Write (14; 7) as a convex combination of (8; 4) and (16; 8). Show your solution.
My Solution: c = (14,7) so maximize z = 14x+7y
Let X1 = (8,14)^T; cX1 = (14,7)(8,14) = 210
Let X2 = (16,8)^Tl cX2 = (14,7)(16,8) = 280
So, the convex combination of maximize z = 210alpha(1) + 280alpha(2) ==> Is that correct?...

E. What is the maximum number of extreme points of a feasible region with only one constraint excluding the nonnegativity constraint?
My solution: I said that the maximum number of extreme points will not exist because if there is no nonnegativity constraint there is no x and y axes.

Thanks:)

FWT
Posts: 153
Joined: Sat Feb 28, 2009 8:53 pm

### Re: Linear Programming quiz questions

E. What is the maximum number of extreme points of a feasible region with only one constraint excluding the nonnegativity constraint?
My solution: I said that the maximum number of extreme points will not exist because if there is no nonnegativity constraint there is no x and y axes.
When they say "excluding the non-negativity constraint", they mean that you've got only one constraint "besides the regular 'the variables can't be negative' constraint". They don't mean that the variables are negative or that there aren't any axes on the graph.

massmatics
Posts: 2
Joined: Mon Sep 14, 2015 9:26 am
Contact:

### Re: Linear Programming quiz questions

Thanks
Is my other solutions okay??..