** Instructions** : Each assignment will include a PDF file (like this one) with the assignment questions and an Excel file, with an Answers sheet and any data or models that we provide you with. You must download the PDF and Excel files. When you have entered your answers in the Answers sheet, then save and upload the Excel file. You must upload the same Excel file you downloaded. Further instructions are provided in the Assignment Submission Guide (see

**in eClass).**

**Assignments**Marking will be based on the answers in the Answers sheet of the file you upload. We will only look at the rest of the file if there is an appeal (and even then, the answers in the Answers sheet take precedence.) If you wish to appeal a mark then the file you uploaded must include your supporting work for each question. For HW1, it is a good idea to make copies of the “Fish” worksheet; one copy for each fish-related question.

Put your answers in the appropriate cells in the Answers sheet. Use ** paste special … values** to for all numerical answers. Follow all instructions provided in the Answers sheet. Save your file with the appropriate name and in the appropriate format (“Excel workbook, * .xlsx”).

** Total points** : 25, of which 2 points are for following the submission instructions provided above.

** Preliminary Questions **(5 pts.)

1. (1 pt.) I understand that I must attend the lab section I am registered in for all lab quizzes.

a. Yes

b. No

2. (1 pt.) I understand that it is my responsibility to read the syllabus and ask for clarification if necessary.

a. Yes

b. No

Here is a list of behaviours to avoid during lectures and labs, so as not to distract other students or the instructor. This list is based, in part, on suggestions from the class during the first lecture.

· Showing up late. If you cannot avoid showing up late (or leaving early) then do so quietly and sit close to an aisle.

· Talking while the instructor is talking.

· Texting, playing Tetris, browsing social media, watching videos, or performing other tasks that are not related to the course using a smartphone, tablet, or other electronic device.

· Not putting phone on silent.

· Coughing or sneezing.

· Eating loudly.

3. (1 pt.) I will do my best to not engage in these behaviours.

a. Yes

b. No

4. (1 pt.) Do you have access to a home computer (desktop or laptop) with an Internet connection?

a. Yes, a Windows PC

b. Yes, a Mac

c. No

d. Yes, other

5. (1 pt.) Do you have MS Office on your computer?

a. Yes, MS Office 2010, 2013, or 2016 for Windows

b. Yes, an older version of MS Office for Windows

c. Yes, MS Office for the Mac

d. No

**Questions about the Fisheries Management model **(18 pts.)

**Questions about the Fisheries Management model**

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

• The lake initially has 5,000 trout

• Carrying capacity = 75,000 trout

• Trout population at the end of August:

P_{Aug} = P_{Apr} + a ´ (1 – (P_{Apr} / capacity)) ´ P_{Apr}, where a = 0.3.

• Each fish can be sold for $12.99 in any year

• The discount rate is 2%

• The planning horizon is 30 years (Year 0 to Year 29)

• At the end of Year 29 (= Year 29 ** August **population – Year 29

**catch), the number of fish left must be at least 40% of the carrying capacity**

**September**

**[only applies to Question 10, not to Questions 7-9]**Create a model in the “Fish” worksheet in the Excel file to answer the following questions. Each question is independent, that is, assumptions made in one question do not carry over to the next question. Do __not__ round your answers.

6. (1 pt.) The April population in Year 19 in the fish model is:

a) An input

b) An output

A ** solution **specifies 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) policy you can.

7. (1 pt.) Solution 1: Catch ** 15,000 fish **each year if the August population is greater than 15,000 fish; otherwise catch nothing. What is the NPV?

8. (1 pt.) Solution 2: Catch ** 11% **of the August population each year. What is the NPV?

9. (1 pt.) Solution 3: Catch ** 15,000 fish every third year **(Years 0, 3, 6, etc.) if the August population in that year is greater than 15,000 fish; otherwise catch nothing. What is the NPV?

10. (12 pts.) Your solution: Find the ** highest NPV **you can. Make sure the fish population does not become negative and that the number of fish left at the end of Year 29 (the 30th year) is at least 40% of the carrying capacity, that is, at least 0.4*75,000 = 30,000. Report the

**(the number of fish to catch each year), the number of fish remaining at the end of Year 29, and the**

**solution****.**

**NPV**The answer to Question 10 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 **(3 pts.): If the solution you report satisfies the constraints that the fish population does not become negative and you have 30,000 or more fish left at the end of Year 29, then you get 3 pts. If your solution satisfies all constraints, then we say that the solution is

*.*

*feasible***·**(2 pts.): If the solution you report is entered into a correct model and the resulting number of fish remaining at the end of Year 29 and the NPV are the same as the one you report, then you get 2 pts.

**Consistency****·**(7 pts.): If the solution you report is feasible

**Optimality**__and__it results in an NPV that is within 5% of the best we have been able to find, then you get 7 pts.

*, when rounded to the closest $1,000. If the NPV of the solution you report is*

*The best solution we were able to find has an NPV of $1,090,000*more than 5% below the highest possible NPV, then you get part marks, between 0 and 7 pts. To get part marks, your policy must result in an NPV that is higher than that from Solutions 1, 2, and 3.

__Hint 1__: If your solution is not feasible, that is, if the fish population becomes negative or if you have less than 30,000 fish left at the end of Year 29, then you get no optimality marks. We will always follow this rule when marking optimization problems.

__Hint 2__ : Keep Question 11 in mind when obtaining your solution to Question 10. That is, try to find a solution that has an NPV that is within 5% of the best possible __and__ is easy to describe.

11. (2 pts.) Describe your solution from the preceding question in ** one sentence** (not to exceed 200 characters). The description should be in English (no formulas), it should enable a person to reconstruct the number of fish to catch each year, and it should be as simple and as brief as possible.

__Hint 1__ : Questions 7, 8, and 9 provide examples of simple and brief descriptions.

__Hint 2__ : You should describe the solution you obtained. You should __not__ describe the method you used to obtain the solution.