A Small Town Wants to Build Some New Recreational Facilities

question 51

Essay

A small town wants to build some new recreational facilities.The proposed facilities include a swimming pool,recreation center,basketball court and baseball field.The town council wants to provide the facilities which will be used by the most people,but faces budget and land limitations.The town has $400,000 and 14 acres of land.The pool requires locker facilities which would be in the recreation center,so if the swimming pool is built the recreation center must also be built.Also the council has only enough flat land to build the basketball court or the baseball field.The daily usage and cost of the facilities in $1,000)are shown below.
Formulate the ILP for this problem.
$$\begin{array} { r r r r r } \text { Variable } & \text { Facilty } & \text { Usage } & \text { Cost \$1,000) } & \text { Land } \\\hline \mathbf { x } _ { 1 } & \text { Swimruine pool } & 400 & 100 & 2 \\\mathbf { x } _ { 2 } & \text { Recreation center } & 500 & 200 & 3 \\\mathbf { x } _ { 3 } & \text { Basketball court } & 300 & 150 & 4 \\\mathbf { x } _ { 4 } & \text { Baseball field } & 200 & 100 & 5\end{array}$$

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Definitions:

Replicability

The ability of a study or experiment to be repeated or reproduced to verify results and confirm reliability and validity of findings.

Illusory Correlation

A cognitive bias where a relationship between two variables is perceived despite no such relationship existing.

Clever Hans Effect

The phenomenon where a person or animal in a study can pick up on subtle, unintentional cues from their interactants, leading to seemingly intelligent responses.

Visual Cues

Environmental or situational indicators that are perceived visually, guiding behavior through visual information.