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# Maximization or minimization of a quantity

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In the graph area problems looking for the steps

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1. The maximization or minimization of a quantity is the

a. goal of management science.
b. decision for decision analysis.
c. constraint of operations research.
d. objective of linear programming.

2. Which of the following is a valid objective function for a linear programming problem?
a. Max 5xy
b. Min 4x + 3y + (2/3)z
c. Max 5x2 + 6y2
d. Min (x1 + x2)/x3

3. A solution which satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called
a. optimal.
b. feasible.
c. infeasible.
d. semi-feasible.

4. To find the optimal solution to a linear programming problem using the graphical method
a. find the feasible point that is the farthest away from the origin.
b. find the feasible point that is at the highest location.
c. find the feasible point that is closest to the origin.
d. none is these is true.

5. The improvement in the value of the objective function per unit increase in a right-hand side is the
a. sensitivity value.
b. dual price.
c. constraint coefficient.
d. slack value.

6. Solve the following system of simultaneous equations.

6X + 2Y = 50
2X + 4Y = 20

a- X = 8, Y = 10
b- X = 8, Y = 11
c- X = 18, Y = 1
d- X = 8, Y = 1

7-10. Use this graph to answer the questions.

Max 20X + 10Y
s.t. 12X + 15Y =< 180
15X + 10Y =< 150
3X - 8Y =< 0
X , Y >= 0

7- Which area (I, II, III, IV, or V) forms the feasible region?

a. Point D
b. Area III
c. Constraints 2 and 3
d. S2 and S3 are equal to 0

8- Which point (A, B, C, D, or E) is optimal?

a. Point D
b. Area III
c. Constraints 2 and 3
d. S2 and S3 are equal to 0

9- Which constraints are binding?

a. Point D
b. Area III
c. Constraints 2 and 3
d. S2 and S3 are equal to 0

10- Which slack variables are zero?

a. Point D
b. Area III
c. Constraints 2 and 3
d. S2 and S3 are equal to 0
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