Mountainside State Park Has Four Visitor Centers $1 \mathrm { E } + 0 \mathrm { wn } + 0 \mathrm { ws } + 0 \mathrm { we } + 0 \mathrm { ww }$

question 28

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 $1 \mathrm { E } + 0 \mathrm { wn } + 0 \mathrm { ws } + 0 \mathrm { we } + 0 \mathrm { ww }$
S.T. 1) $- 400 \mathrm { E } + 400 \mathrm { wn } + 1200 \mathrm { ws } + 2400 \mathrm { we } + 1500 \mathrm { ww } < 0$
2) $- 3 E + 3 w n + 6 w s + 10 w e + 7 w w < 0$
3) $- 56 \mathrm { E } + 56 \mathrm { wn } + 108 \mathrm { ws } + 92 \mathrm { we } + 108 \mathrm { ww } < 0$
4) $- 49 \mathrm { E } + 49 \mathrm { wn } + 83 \mathrm { ws } + 56 \mathrm { we } + 72 \mathrm { ww } > 0$
5) $- 38 \mathrm { E } + 38 \mathrm { wn } + 425 \mathrm { ws } + 1200 \mathrm { we } + 630 \mathrm { ww } > 0$
6) $+ 1 w n + 1 w s + 1 w e + 1 w w = 1$
OPTIMAL SOLUTION
Objective Function Value = 1.000 $$\begin{array} { c c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { E } & 1.000 & 0.000 \\\text { wn } & 1.000 & 0.000 \\\text { ws } & 0.000 & 0.000 \\\text { we } & 0.000 & 0.000 \\\text { ww } & 0.000 & 0.000\end{array}$$ $$\begin{array} { c c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 0.000 & 0.008 \\2 & 0.000 & 0.000 \\3 & 0.000 & 0.001 \\4 & 0.000 & - 0.034 \\5 & 0.000 & - 0.013 \\6 & 0.000 & - 1.000\end{array}$$

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Definitions:

Net Sales

The amount of sales revenue left after deducting sales returns, allowances, and discounts.

Cash Basis

An accounting method where revenues and expenses are recorded only when cash is received or paid, respectively.

Earned Revenues

Income generated from the normal business operations after the delivery of goods or services to customers.

Prepaid Costs

Expenses paid in advance for goods or services to be received in the future, recorded as assets until they are consumed.