# When solving an IP (integer program) with LP relaxation rounding could result in

When solving an IP (integer program) with LP relaxation rounding could result in…

Answer

An Infeasible solution.

A suboptimal solution.

An optimal solution.

All of the above.

A well-defined decision variable…

Answer

Contains a min or max.

Contains a quantity, a noun, a verb, and a time period.

Is what is holding you back from your goal.

All of the above

When making a mathematical model there is a tradeoff between how well it…

Answer

Represents real world and how easy it is to solve.

Uses mathematical symbols and how well it represents reality.

Represents iconic models and analog models.

Communicates with computers and humans

Cintis Coal’s accounting manager has been tasked by the CEO to determine which mines the company should open in the next 5 years. He has worked with other departments to estimate the cost of opening each mine as well as the total expected return on investment over the next 15 years. The CEO wants to allocate only $2,000,000 over the next five years for opening the mines. The accounting manager needs to maximize the return while staying within the budget. The cost and return for each project is listed below.

Mine Cost (in $1000) Return (in $1000)

1 $300 $600

2 $400 $1000

3 $450 $650

4 $600 $1200

5 $800 $1400

6 $1200 $2000

Let Xi = 1 if mine i is selected and 0 otherwise. i = 1,2,3,4,5,6

Max Return Z = 600 X1 + 1000 X2 + 650 X3 + 1200 X4 +1400 X5 + 2000 X6

St

300X1 +400 X2 + 450 X3 + 600 X4 + 800 X5 + 1200 X6 <= 2000

Xi = 0 or 1 for all i

The manager has determined that at most Cintis Coal wants to open 2 mines that do not return at least double the cost of opening the mine in the first 15 years. Write a constraint for this.

Answer

X5 + X6 <= 2

X3 + X5 + X6 <= 1

X3 + X5 +X6 <= X1 + X2 + X4

X3 + X5 + X6 <= 2

Mine 5 can only be selected if mine 4 is selected and mine 6 can only be selected if mine 5 is not selected. Write two constraints for these.

Answer

X4 <= X5 and X6 + X5 <= 1

X5 <= X4 and X6 – X5 <= 1

X5 <= X4 and X5 + X6 <= 1

X6 <= X5 and X4 + X5 <= 1

The $600 return on investment for mine 1 in this problem is a….

Answer

Parameter

Constraint

Objective Function

Decision Variable

Graph the following linear program to find the solution.

Let X = the number of hats to produce

Y = the number of shirts to produce

Max Profit Z = 3X+6Y

St. 7X+14Y>=14 (1)

4X+5Y<=20 (2)

X+Y <=7 (3)

X<=4 (4)

X,Y>=0

How many extreme points are there in the feasible region?

Answer

5

6

4

3

Which constraints are redundant constraints?

Answer

(3) and (4)

(4)

None are redundant

(3)

What is the optimal number of hats and shirts to produce?

Answer

Producing 4 hats and 0 shirts is optimal.

Producing 4 hats and 1 shirt is optimal.

Producing 2 hats and 0 shirts is optimal.

Producing 0 hats and 4 shirts is optimal.

Which constraints are binding?

Answer

(4)

(2) and (4)

(2)

(1)