Linear Programming (Inequalities)

1. Consider the simplex tableau

x y u v w M

[ 1 0 3 0 0 0 | 10]

[ 0 0 1 0 1 0 | 0]

[ 0 1 -6 0 0 0 | 3]

[ 0 0 8 1 0 0 | 7]

[ 0 0 5 0 0 1 4]

The tableau above is the final one in a problem to minimize –x + 2y.
The minimum value of –x + 2y is:

-10

-4

0

4

none of the above

2. The inequality 2x – y + 5z (greater than or equal to symbol) -6 is
equivalent to the inequality

2x – y + 5z (less than or equal to symbol) -6

2x – y + 5z (greater than or equal to symbol) 6

-2x + y – 5z (less than or equal to symbol) -6

-2x + y -5z (greater than or equal to symbol) 6

none of the above

Consider the following linear programming problem: A workshop of
Peter’s Potters makes vases and pitchers. Profit on a vase is $3;
profit on a pitcher is $4. Each vase requires Ð… hour of labor, each
pitcher requires 1 hour of labor. Each item requires 1 unit of time in
the kiln. Labor is limited to 4 hours per day and kiln time is limited
to 6 units per day. Initial and final tableaux are shown in finding
the production plan which will maximize profits: (x = number of vases
and y = number of pitchers made per day).

x y u v M

[ -1 1 1 0 0 | 4 ]

[ 2 | ]

[ 1 1 0 1 0 | 6 ]

[-3 -4 0 0 1 | 0 ]

(initial)

x y u v M

[ 0 1 2 -1 0 | 2 ]

[ 1 0 -2 2 0 | 4 ]

[0 0 2 2 1 | 20 ]

(final)



If kiln time were decreased by one unit per day, determine the optimal
performance schedule.

x = 3, y = 4

x = 4, y = 2

x = 6, y = 1

x = 2, y = 3

none of the above





In a linear programming problem in a standard from, the initial and
final tableaux are given as below:

x y u v M

[ 1 3 1 0 0 | 50 ]

[ 1 5 0 1 0 | 70 ]

[-6 -24 0 0 1 | 0 ]

(initial)

x y u v M

[ 0 1 2 -5 -3 | 20 ]

2 2

-1 1

[ 1 0 2 2 0 | 10 ]

[0 0 3 3 1 | 360]

(final)

Given that x (greater than or equal to sign) 0 and y (greater than or
equal to sign) 0, if h units were added to the first resource, the
maximum value of the objective function is

360

360 + 3h

360 + h

360 + h(to the 5th power)/2

none of the above

5. To solve the linear programming problem

Minimize 50x + 70y subject to:

x + y (greater than or equal to symbol) 6

3x + 5y (greater than or equal to symbol) 24 we can use the simplex
method on its dual.

x (greater than or equal to symbol) 0 , y (greater than or equal to
symbol) 0

The objective function of the dual is

u + 3v

u + 5v

6u + 24v

70u + 50v

none of the above