LP Incinerator Example
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This page describes a solution to problem 11.1 on page 191 of Stokey-Zeckhauser text.
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Problem 11.1 Incinerators

Burtonville burns 3000 tons of trash per day in three elderly incinerators. All three have antipollution devises that are less than satisfactory. Their emission profiles differ as shown in Table 11-2. At present all three incinerators are operating at full capacity. The remainder of the city's trash, another 1500 tons per day, is dumped in a sanitary landfill area. This is a much more expensive method of disposal. The state's Environmental Quality Commission has brought suit against the city; the Superior Court has issued a temporary restraining order under which sulfur dioxide emissions must be limited to 400,000 units per day and particulate emissions to 50,000 units per day. What is the most economical way to make the necessary cutbacks?

Table 11-2 Emissions per ton burned

Incinerator Capacity in tons/day Units of SO2 Units of Particulate
A 1,200 250 20
B 800 150 30
C 1,000 220 24

Objective Function. Minimize $4500-X_A-X_B-X_C$.

Subject to constraints:

(1)
\begin{align} X_A \leq 1200, X_B \leq800, X_C \leq 1000 \end{align}
(2)
\begin{align} 250X_A+150X_B+220 X_C \leq 400,000 \end{align}
(3)
\begin{align} 20X_A+30 X_B+24 X_C \leq 50,000 \\ \end{align}