he council wants to construct the facilities that will maximize expected daily u
ID: 325490 • Letter: H
Question
he council wants to construct the facilities that will maximize expected daily usage by the residents of the community subject to land and cost llimitations. The usage, cost, and land data for each facility are listed below. The community has $240,000 construction budget and 24 arces of land. Because the swimming pool and tennis center must be built on the same part ot the land parcel, however, only one of these two facilities can be constructed. Formulate an optimization mode to assist the council in making its decision. Q1)Write out any constraints necessary for this problem in terms of the decision variables defined above. Q2) A very inluential citizens group has made it clear that it strongly prefers the athletic fielld to the gynnasim; thus the council will not approve the gymnasium unless the athletic field is also approved. How can the model be modified to incorporate this condition? Q3) The mayor has deicded that no more than three of the facilities may be constructed wiht funds from this year's budget. How can the model be modified to incorporate this comdition? Please use Solver(EXCEL) to define Q2 and Q3
expected usage facility people/day cost($) Land requirements (acres) swimming pool 600 70,000 8 tennis center 180 20,000 4 athletic field 800 50,000 14 gymnassium 300 180,000 6Explanation / Answer
Q1) The constraints necessary would be to further streamline budgets and impose cuts to ensure maximum utilisation of resources at the same time implement all conditions necessary for benefitting maximum people while working within these constraints.
Firstly considering optimal utilistion and allocation of resources with reference to land allocation only the swimming pool or the tennis court can be constucted.
Total land available= 24 acres less 8 acres needed for pool we have 16 acres. Options for allocation of 16 acres is either 14 acres to athletic field or 6 acres to gymnasium as construction of both would require 20 acres.
Now second option would be if we construct tennis center 24 acres minus 4 acres so balance land is 20 acres which is sufficient for construction of both other facilities of athletic field and gymnasium.
Hence, for optimum utilisation of land resources we need to construct a tennis center, an athletic field and a gymnasium.
Q2) Let us consider allocation of funds. For the above three facilities total funds required would be
20,000+50,000+180,000=$250,000
Funds available = $240,000. Therefore, there is a shortage of $10,000. The Influential Citizens group can be assured that the athletic field will be constructed provided they could provide a donation of $10,000. Any shortage in this amount will have to be managed with reduction in budget of the gymnasium as that is consuming a large chunk of the financial resources.
3) The mayor's decision is not only sensible but it's implementation becomes mandatory because the inherent constraints of land resources clearly state that only one facility can be built on the same land parcel either the pool or the tennis court. Secondly, the financial constraints would cause too many budgetary cost cuts to be imposed for set-up resulting in low grade facilities leaving the residents dissatisfied, as also being potentially dangerous. To balance the usage with resources spent the council has to however, ensure that usage of the gymnasium is encouraged and more members enroll for services.
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