These questions are based on the model that we discussed in the lecture. Some input parameters have

been changed.

• The lake currently has 25,000 trout
• Carrying capacity = 150,000 trout
• Trout population at the end of August:

PAug= PApr+ a(1-(PApr/ capacity))PApr, wherea = 0.40

• Each fishing license can be sold for $12.99 in any year
• The discount rate is 3%
• The planning horizon is 15 years (Year 0 to Year 14)
• The end-of-horizon population should be at least 10,000.

6. (1 pt.) The"number of fish to catch in the first year"in the fish model is:

1. a)An input
2. b)An output

Asolutionspecifies the number of fish to catch each year. In the remaining questions, we ask you to evaluate three solutions and finally we ask you to find the best (highest NPV) solution you can.

Note 1:It is a good idea to make copies of the"Fish" worksheet; one copy for answering and showing your work for each question. Each question is independent, that is, assumptions made in one question do not carry over to the next question.

Note 2:The number of fish can be fractional. Do not round your answers.

1. (2 pts.) Solution 1: Catch20,000 fisheach year if the August population is greater than or equal to
2. 40,000fish; otherwise catch nothing. What is the NPV?
3. (2 pts.) Solution 2: Catch80%of the population growth each year. What is the NPV?
4. (2 pts.) Solution 3:Wait until the last yearand then catchall except 10,000 fish in the last year. What is the NPV?
5. (12 pts.) Your solution: Find thehighest NPVyou can. Make sure that:

• The fish population does not become negative, and
• You have 10,000 or more fish left at the end of Year 14 (the beginning population of Year
• 15).
• Report thesolution(the number of fish to catch each year) and theNPV.
• Your answer will be marked based on the following three criteria. (We will use the same approach throughout the course to mark solutions to optimization problems.)

Feasibility(4 pts.): If the solution you report satisfies the constraints that the fish population does not become negative and you have 10,000 or more fish left at the end of Year 14, then you get the marks for feasibility. If your solution satisfies all constraints, then we say that the solution isfeasible.

Page 2 of 3

OM 352, Fall 2019 HW 1 Assigned: 5 Sep. 2019 Due: 11:59 PM, 11 Sep. 2019

• Consistency(3 pts.): If the solution you report is entered into a correct model and the resulting NPV is the same as the one you reported, then you get the marks for consistency.
• Optimality(5 pts.): If the solution you report is feasible and it results in an NPV that is within 5% of the best we have been able to find, then you get the marks for optimality.The best solution we were able to find has an NPV of $2,160,000, when rounded to the closest $1,000. If the NPV of the solution you report is between 5% and 15% below the highest possible NPV, then you get part marks.
• Note 3:If your solution is not feasible, that is, if the fish population becomes negative or if you have less than 10,000 fish left at the end of Year 14, then you getNOoptimality marks. We will always follow this rule when marking optimization problems.