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

been changed.

$$ The lake currently has $5,000$ trout

$$ Carrying capacity $=90,000$ trout

$$ Trout population at the end of August:

PAug $=$ PApr $+$ a $(1($PApr $/$ capacity$))$ PApr, where a $=0\mathrm{.}4$

$$ Each fishing license can be sold for $$14\mathrm{.}99$ in any year

$$ The discount rate is $5\%$

$$ The planning horizon is $31$ years $($Year $0$ to Year $30)$

$(2$ pts$.)$ Solution $1$: Catch $6,000$ fish each year if the August population is greater than or equal to

$25,000$ fish; otherwise catch nothing. What is the NPV$?$

$8.(2$ pts$.)$ Solution $2$: Catch $25\%$ of the August population each year. What is the NPV$?$

$9.(2$ pts$.)$ Solution $3$: Catch no fish in the first $10$ years $($Year $0$ to Year $9),$ catch $30\%$ of the August

Population each year for the next $20$ years $($Year $10$ to Year $29),$ and all but $9,000$ fish in the last year

$($Year $30).$ What is the NPV$?$

$10.(10$ pts$.)$ Your solution: Find the highest NPV you can. Make sure that:

$$ The fish population does not become negative, and

$$ You must have $9,000$ or more fish left at the end of Year $30($the beginning population of

Year $31).$