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

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 = 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.

L1+L2=20

a) Determine the total daily fish catch at the lakes

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

Q1 = XXXXXXXXXX)^2 = 120

Q2 = XXXXXXXXXX)^2 = 90

Total fish = 210

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

16 – 2x.04l1 = 16=.8l1

16/.8 = 20 10/.2 = 50

Q1= XXXXXXXXXX)^2 = 160 Q2= XXXXXXXXXX)^2 = 0

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

L1+L2=15

Extra Credit: Offer any insightful comments that you glean from analyzing a problem such as this one.

Robert · Accepted Answer

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 = 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.

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: Q 1 = 16L 1 - 0.4L 1 2 and Lake 2: Q...

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