$(5)$ A local authority has to decide on the location of a new waste$-$disposal facility and five sites are currently being considered: Inston Common, Jones Wood,Peterton, Red Beach and Treehome Valley. In order to help them choose between

the sites, the managers involved in the decision arranged for a decision analyst

to attend one of their meetings. He first got the managers to consider the factors

which they thought were relevant to the decision and, after some debate, four

factors were identified:

$($i$)$ The visual impact of the site on the local scenery $($for example, a site at

Treehome Valley would be visible from a nearby beauty spot$).$

$($ii$)$ The ease with which waste could be transported to the site $($for example,

Red Beach is only $2$ miles from the main town in the area and is close to a

main highway, while Inston Common is in a remote spot and its use would

lead to a major increase in the volume of transport using the minor roads

in the area$).$

$($iii$)$ The risk that the use of the site would lead to contamination of the local

environment $($e$.$g$.,$ because of leakages of chemicals into watercourses$).$

$($iv$)$ The cost of developing the site.

The decision analyst then asked the managers to assign scores to the sites

to show how well they performed on each of the first three attributes. The

scores they eventually agreed are shown below, together with the estimated

cost of developing each site. Note that $0$ represents the worst and $100$ the

best score on an attribute. In the case of risk, therefore, a score of $100$ means

that a site is the least risky.

$\backslash$table$[[,$Benefit,$],[$Site$,$Visual impact,$\backslash$table$[[$Ease of$],[$transport$]],$Risk,Costs $($$ m$)],[$Inston Common,$100,0,60,35],[$Jones Wood,$20,70,100,25],[$Peterton$,80,40,0,17],[$Red Beach,$20,100,30,12],[$Treehome Valley,$0,70,60,20]]$

The decision analyst then asked the managers to imagine a site which had the

worst visual impact, the most difficult transport requirements and the highest

level of risk. He then asked them if they had a chance of switching from this

site to one which had just one of the benefits at its best value, which would

they choose? The managers agreed that they would move to a site offering the

least risk of contamination. A move to a site with the best visual impact was

considered to be $80\%$ as preferable as this, while a move to one with the most

convenient transport facilities was $70\%$ as preferable.

$($c$)$ Assuming that mutual preference independence exists between the at$-$

tributes, determine the value of aggregate benefits for each site.

$($d$)$ Plot the aggregate benefits and costs of each site on a graph and hence iden$-$

tify the sites which lie on the efficient frontier.

$($e$)$ Although a weight of $80$ was finally agreed for visual impact, this was

only after much debate and some managers still felt that a weight of $65$

should have been used while others thought that $95$ would have been

more appropriate. Perform a sensitivity analysis on the weight assigned to

visual impact to examine its effect on the aggregate benefits of the sites and

interpret your results.

Please Answer the following question part C$,$ D$,$ E$,$ for Quantitave Business Analysis