Question

The City of Lake Orion issues licenses to 20 individuals to fish in its two lakes.

The daily fish catch at Lakes 1 and 2 respectively are given as follows:

Lake 1:Q₁ = Q₁ = 16L₁- 0.4L₁² and Lake 2: Q₂ = 10L₂ - 0.1L₂²,

where Q is the fish catch, and L is the number of fishermen, at a given lake.

a) Determine the total daily fish catch at the lakes

(i) if equal numbers of fishers fished in each of the two lakes.

(ii) if the 20 fishermen want to maximize their joint (or total) fish catch.

b) Determine how the fishermen should allocate themselves if only 15 of them were licensed to fish the lakes.

PART 2: Offer any insightful comments that you glean from analyzing a problem such as this one. [You might try some "outside of the box" thinking here. E.g., suppose we change this problem to 20 one-day licenses, and YOU are the only one interested in fishing in these lakes. You can "choose to buy" all 20 licenses. Would any outcomes be different?]

Answer 1