Background:

A small community of N persons $($see below to calculate N$)$ is interested in creating a town$-$wide

water supply. They have hired an engineering consultant to look at some options. After

considerable research, the engineer has provided the town with the following information:

$$ An average resident$$s usage $($Qp$)$ is $140$ gpd $($gallons per day$).$

$$ There are two feasible water sources for the town $($sources A and B$),$ either of which could

provide enough water.

$$ Source A is a deep well into the aquifer. The cost function using the water from the

aquifer is:

$$

$=$

$2$

$106$

$$

$+395$

where VA is the volume of water drawn from source A in gallons and Y is a coefficient below.

$4900$

$$ Source B is a nearby lake and the cost function for water from this source is:

$$

$=$

$5000$

$+410$

where VB is the volume of water drawn from source B in gallons.

C is the total cost of water from both sources in dollars, C $=$ CA $+$ CB$.$ V $=$ VA $+$ VB is the total

volume of water being pulled on a given day.

The value of N and the coefficient Y can be calculated as:

N $=$ sum$($my$\_$name$).\{$Use your own first name here.$\}$

Y $=$ round$($N$/8).$

Problem Statement:

The objective of this lab is to determine the lowest cost option for the town$$s water supply. This

is an optimization problem. You will need to write a function that determines the total cost to the

town based on how many people are using each source $($A or B$).$ The function should look

something like this when it is run:

$>>$total$\_$cost $=$ my$\_$cost$\_$function$($NA$,$ N$)\{$enter$\}$

total$\_$cost $=58000$

where NA is the number of people pulling from source A and N is the total number of people.

$($The function should calculate how many people are pulling from source B automatically.$)$

You will then need to write a script that runs your function for the range of possible values of NA

to determine the best option for the town. Your script should also plot total$\_$cost vs$.$ NA$.$ To

create your figures, use the function plot $($check doc plot for more information$).$

Use your code to answer the following questions:

$1.$ How many people should use each source to minimize the cost to the town?

$2.$ Rerun your code for a population of N $=500$ persons. How many people should use each

source now?