Math 123 exam 2

Some LP problems have exactly two solutions.

False

The following LP problem has an unbounded physical region: c=x-y 4x-3y<0 3x-4y>0

False

No LP problem with an unbounded region has a solution

False

The following LP problem has an unbounded region: c=x-y 4x-3y<0 x+y<10

False

The following LP problem has an unbounded region: c=x-y 4x-3y<0 x+y>10

False

The following LP problem has an unbounded region: c=x-y 4x-3y>0 3x-4y<0

True

If a feasible region is empty, then it is bounded.

True

The solution set 2x-3y<0 is below the line 2x-3y=0

False

There is at least 3 more grams of x than y

X-y>3

There is at least 3 times the grams of x than y

X-3y>0

There is no more grams of x than y

X-y <0

The following has an empty feasible region:C=x-y4x-3y<03x-4y>0

False

In simplex method, a basic solution can assign zero to basic variables

True

In feasible solution all variables are nonnegative

True

In feasible solution all variables are positive

False

Choosing the pivot column by requiring that it be the column with the most negative entry to the left of the vert line in the last row of the tableau ensures that there's no iteration with greatest increase or decrease to objection function

True

Choosing the pivot column by requiring that it be the column with the largest positive entry to the left of the vert line in the last row of the tableau ensures that there's no iteration with greatest increase or decrease to objection function

False

In final tableau if the problem has a solution, the last column will have no negative numbers above the bottom row

True

In final tableau if the problem has a solution the last column will contain no negative numbers

False

Choosing the pivot row by requiring that the ratio associated with that row be the smallest non negative number ensures that the iteration will not take is from a feasible point to non feasible

True

The optimal value attained by the objective function for the primal problem may be different from that attained by dual

False

Dual of standard min must be a standard max

False

The dual of stand min with nonnegative obj function coefficients is a standard max problem

True

In stand max, each constraint inequality may be written so that it is less than or equal to a nonnegative number

True

In stand max, the obj function must have nonnegative coefficients

False

In standard min, the obj function must have nonnegative coefficients

False

In stand min, each constraint inequality may be written so that it is greater than or equal to any real number

True

If stand max has no solution, then the feasible region is emoty

False

If stand max has no solution then the feasible region is unbounded

True