1. The constraint 5x1 - 2x2 < 0 passes through the point (xx, 50).
xx = ?

5x1-2x2=0
5x1 = 2 x2 = 2 * 50 =100
x1= 100/5 =20
xx=20

Answer: xx=20

2. In a linear programming problem, the binding constraints for the optimal solution are
5X + 3Y < 30
2X + 5Y < 20
Fill in the blanks in the following sentence:
As long as the slope of the objective function stays between _______ and _______, the current optimal solution point will remain optimal.

A. 1/3 and 3/5
B. -5/3 and -4/5
C. -8/3 and -2/5
D. -5/3 and -2/5

Answer: D. -5/3 and -2/5

The slope of 5X + 3Y < 30 is -5/3
The slope of 2X + 5Y < 20 is -2/5
As long as the slope of the objective function stays between _-5/3_ and __-2/5___, the current optimal solution point will remain optimal.

3. Which of the following could be a linear programming objective function?
A. Z = 1A + 2B / C + 3D
B. Z = 1A + 2BC + 3D
C. Z = 1A + 2B + 3C + 4D
D. Z = 1A + 2B2 + 3D
E. all of the above

Answer: C. Z = 1A + 2B + 3C + 4D

The objective function should be linear
Z = 1A + 2B / C + 3D ----- B/C is not linear (division)
Z = 1A + 2BC + 3D ----- BC is not linear (product)
D. Z = 1A + 2B2 + 3D ---- B^2 is not linear (square term)

4. Output from a computer package is precise and answers should _______ be rounded.
A. never
B. always
C. sometimes
D. often

Answer: D. often

5. Mark the answers below which are true:
A. Bayes probability uses updates to improve estimates of prior probabilities.
B. Shafer-Dempster probabilities use belief functions which are very useful for situations when the sum of existing knowledge (probabilities) need not add to one.
C. Fuzzy logic is too inaccurate to be used for anything useful.
D. Both A and B
E. All of the above

Answer: D. Both A and B

Bayes' theorem tells how to update or revise beliefs in light of new evidence.

Dempster-Shafer theory is designed to cope with varying levels of precision regarding the information. It allows for the direct representation of uncertainty where an imprecise input can be characterized by a set or an interval and the resulting output is a set or an interval.

Fuzzy logic deals with reasoning that is approximate. But approximate does not mean that it is too inaccurate. Fuzzy logic has applications.
Fuzzy logic can be used to control household appliances such as washing machines (which sense load size and detergent concentration and adjust their wash cycles accordingly) and refrigerators. (source: Wikipedia)