Mountainside State Park Has Four Visitor Centers

question 19

Essay

Mountainside State Park has four visitor centers. To study the operation of these centers, a DEA model has been developed that compares inputs (size, number of staff, weekly hours of operation) and outputs (% of visitors attending educational program, daily sales in gift shop). The computer solution is shown below. What can you conclude about the efficiency of the North center?
LINEAR PROGRAMMING PROBLEM
MIN
1E+0wn+0ws+0we+0ww
S.T.
1) -400E+400wn+1200ws+2400we+1500ww<0
2) -3E+3wn+6ws+10we+7ww<0
3) -56E+56wn+108ws+92we+108ww<0
4) -49E+49wn+83ws+56we+72ww>0
5) -38E+38wn+425ws+1200we+630ww>0
6) +1wn+1ws+1we+1ww=1
OPTIMAL SOLUTION
Objective Function Value = 1.000 $$\begin{array} { c c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { E } & 1.000 & 0.000 \\\text { wn } & 1.000 & 0.000 \\\text { ws } & 0.000 & 0.000 \\\text { we } & 0.000 & 0.000 \\\text { ww } & 0.000 & 0.000\end{array}$$ $$\begin{array} { c c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 0.000 & 0.008 \\2 & 0.000 & 0.000 \\3 & 0.000 & 0.001 \\4 & 0.000 & - 0.034 \\5 & 0.000 & - 0.013 \\6 & 0.000 & - 1.000\end{array}$$

---

Definitions:

Willingness To Pay

The maximum amount an individual is prepared to spend on a good or service, indicating the value they derive from the item.

Marginal Cost

The money required to produce another unit of a product or service.

Public Good

A benefit of goods or services, free of charge to everyone in society, provided by public authorities or private organizations or individuals, without seeking financial gain.

Samuelson's Theory

Refers to Paul Samuelson's economic theories, particularly his contributions to public goods, welfare economics, and consumption theory.