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)
