# Essay/Calculation problem: aggregate score/determine which sites lie on the efficient frontier

I’m stuck on a Mathematics question and need an explanation.

Please provide full references for sources cited, if any.

Problem #1 (20 points)

The board of directors of Tolford sports club are searching for a location for their new stadium and they are using the Simple Multiattribute Rating Technique (SMART) to help them with their decision. Five possible sites are being considered and the decision between them will be based on five attributes: (i) the COST of developing the site; (ii) the DISTANCE of the site from downtown Tolford; (iii) the amount of space for car PARKING; (iv) the extent to which choosing the site would cause inconvenience for local RESIDENTS; and (v) the ACCESSIBILITY of the site from the highway network.

The board has assigned scores for each site to measure its performance on the non-monetary attributes. These are shown below, together with the development costs of the sites (note that 0 is the score for the worst site on a given attribute and 100 a score for the best site on that attribute).

 Site Distance Parking Residents Accessibility Cost(\$m) Egbert Heath 10 100 70 50 80 Lakeside 40 80 100 100 65 Jones Street 60 10 0 0 30 The Causeway 0 60 40 60 100 Hodge Street 100 0 20 10 75

The board then considered a hypothetical site that had the worst performance on all the non-monetary attributes. They were then asked, if they could make just one improvement to this site so that it was as good as the best site on this attribute, which improvement would they make? They agreed that they would most prefer to â€œimproveâ€ the DISTANCE from downtown Tolford. Similar improvements in relation to the attributes PARKING, RESIDENTS and ACCESSIBILTY were thought to be, respectively, 30%, 55% and 15% as important as this. It can be assumed that the attributes are mutually preference independent.

(a)The aggregate scores of the first four sites in the above table for the non-monetary attributes are shown below:

 Site Aggregate Score Egbert Heath Lakeside Jones Street The Causeway 43.0 67.0 31.5 24.5

Calculate the score for the Hodge Street site.

(b)Determine the sites which lie on the efficient frontier, when the development costs are brought into consideration, and explain how you arrived at your answer.

(c)The board would be prepared to pay \$18 million to improve the space for PARKING from that equivalent to the worst site for parking to that equivalent to the best, all else remaining equal. Stating any assumptions you have made, determine which site they should select.

(d)The attribute that the board considered to be most important was assigned the lowest weight in the analysis. Explain why the decision model might still accurately reflect the board’s preferences.

Essay/Calculation problem: aggregate score/determine which sites lie on the efficient frontier

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