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 X

_{1}and X

_{2}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 X

_{1}= (8,14)^T; cX

_{1}= (14,7)(8,14) = 210

Let X

_{2}= (16,8)^Tl cX

_{2}= (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:)