Question

The city of Ventura would like to build a seawall to protect the city from the threat of tsunamis. Each additional inches of height further protects the city and the 100 residents are each willing to pay $10 per inch of seawall height, regardless of how many inches are provided. The cost of building a wall that is i inches high is given by c(i) = 6i^2. What is the Pareto Optimal height for the seawall?

Answer 1

Answer:

The Pareto Optimal height is  $i = 100 \ inch$

Step-by-step explanation:

The Pareto Optimal height is a height  of the seawall at which an increase in wall height will exceed the amount the resident are willing to pay and a decrease will affect the protection of the city

The number of residents is $n = 100$

The amount each are willing to pay is  $z=$$10 per inch

 The cost of building a wall that is i inches high is given by $c(i) = 6i^2.$

The total amount the residents are willing to pay is

          $n = 100 * 10$ =  $1000

The maximum cost  is mathematically represented as

                $\frac{dc(i)}{di} = 10i$

which implies that

          1000 =  10i

Hence the Pareto Optimal height is

=>         $i = \frac{1000}{10}$

             $i = 100 \ inch$