QUESTION 1

1. With respect to optimization modelling, which of the following statements are TRUE?

   		The three components of an optimization problem are decision variables, the objective function, and constraints
   		The objective function and constraint functions are expressed in terms of the decision variables
   		The objective of an optimization problem can be to either maximize or minimize the value of the objective function
   		All of the above

QUESTION 2

1. With respect to the feasible region of a linear optimization problem, which of the following statements are FALSE?

   		The feasible region is the set of all values of the decision variables that satisfies the constraints
   		The feasible region is the set of all optimal values of the decision variables
   		For the constraint 4x+5y 200, the boundary line for the feasible values of (x, y) that satisfies this constraint is given by 4x+5y=200

QUESTION 3

1. Is this a linear optimization problem? Min Z = x + y + z 1 Subject to: x y 5 y + z 8 z x 3

   		Yes
   		No

QUESTION 4

1. Is this a linear optimization problem? Max Z = xy 1 Subject to: x-y² 5 0 y 3 x2

   		Yes
   		No

QUESTION 5

1. Plot the following set of constraints of a linear program on a graph: 4x + 4y 160 X + y 50 X0, Y0

   What is the shape of the feasible region for the linear program?

   		Line
   		Triangle
   		Rectangle
   		No feasible region

QUESTION 6

1. The cost of advertising slots on Channel 1 and Channel 2 are $45k and $65k. The total available advertising budget for your company is $1.0 million. If you decide to place x number of advertisements on Channel 1 and y on Channel 2, how would you express this as a mathematical constraint?

   		45y + 65x 1000
   		45x + 65y 1000
   		45x 1000 and 65y 1000
   		45x + 65y 1000