TASK-2-Optimization
Christine Dewi
The following linear programming (LP) or mixed-integer linear programming (MILP) examples
are taken from a textbook. Each example describes a business optimization problem.
For each problem, write down what is/are the decision(s) the business needs to make. Then,
write down as many classes of business requirement as you can identify from these
examples.
Responses:
Q1.
Factory Pollutant 1 (tons) Pollutant 2 (tons)
Cost $
1
0.10
0.45
15
2
0.20
0.25
10
3
0.40
0.30
20
Decision Business: How many pollutions should be reducing each month from each of the three
factories. Minimize the cost of reducing pollution by the desired amounts. Decision Variable:
Two decision variable (pollutant 1 and pollutant 2) for each factory (6 decision variables in total).
Business Requirement (Constraints):
1. Reduce the amount of pollutant 1 in the river by at least 30 tons.
2. Reduce the amount of pollutant 2 in the river by at least 40 tons.
Q2.
Decision Business: How many pig valves should be ordered each month from each of the three
suppliers. Minimize the cost of acquiring the needed valves. Decision Variable: One decision
variable for each supplier (3 decision variables in total).
Business Requirement (Constraints):
1.
2.
3.
4.
At least 500 large valves must be purchased each month.
At least 300 medium valves must be purchased each month.
At least 300 small valves must be purchased each month.
At most 700 valves per month can be purchased from each supplier.
Q3.
Decision Business: How many foods 1 and food 2 Peg need to buy to meet their daily nutritional
requirements. Decision Variable: One decision variable for each food (2 decision variables in
total for food 1 and food 2).
Business Requirement (Constraints):
1. The family needs at least 12 units of vitamin A and 6 units of vitamin C.
Q3
Decision Business: How many lb of gold and silver need to find in each mine as little time as
possible in the mines. Decision Variable: Two decision variable for each mine (4 decision
variables in total).
Business Requirement (Constraints):
1. Goldilocks needs to find at least 12 lb of gold and 18 lb of silver to pay the monthly rent.
Q4
Decision Business: Maximize the total defensive ability of the starting team. Decision Variable:
one decision variable for each player (7 decision variables in total).
Xi = 1 if player # i is selected for the line-up, else 0
Business Requirement (Constraints):
1. The number of players selected must be exactly 7
2. At least 4 members must be able to play guard.
3. At least 2 members must be able to play forward.
4. At least 1 member must be able to play center.
5. The average ball-handling level of the starting lineup must be at least 2:
6. The average shooting level of the starting lineup must be at least 2:
7. The average rebounding level of the starting lineup must be at least 2:
8. If player 3 starts, then player 6 cannot start.
9. If player 1 starts, then players 4 and 5 must both start.
10. Either player 2 or player 3 must start.
Q5