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Answer:
a) attached below
b) stable equilibria = x = 0.1 , x = 0.8
unstable equilibria = other value except 0.1 , 0.8
c) 0.5 , 0.6
Explanation:
Benefit of using the local roads = 1 + 8x - 9x^2
Benefit of using the free way = 3.6
a) Attached below is the required graph
<u>b) Determine The possible equilibrium traffic patterns from the graph </u>
stable equilibria : x = 0.1 , x = 0.8 ( this id because at these given value the benefits of using either routes is equal )
unstable equilibria : every other value of X except 0.1 and 0.8
<u>c) Determine the value of x that maximizes the total benefit to the population</u>
The value of X that maximizes the total benefit to the population = 0.5 and 0.6
attached below is the detailed solution
