OR$2323$ Midterm Examinations

Problem #$1$

Angeles Electric Corporation provides electric power for three cities. The company has four electric gensets that are used to provide electricity. The main generator operates $24$ hours per day, with an occasional shutdown for routine maintenance. Three other gensets $,$ and $3)$ are available to provide additional power when needed. A startup cost is incurred each time one of these gensets is started. The startup costs are $$6,000$ for $1,$$$5,000$ for $2,$ and $$4,000$ for $3.$

These gensets are used in the following ways: A generator may be started at $6$:$00$ A$.$M$.$ and run for either $8$ hours or $16$ hours, or it may be started at $2$:$00$ P$.$M$.$ and run for $8$ hours $($until $10$:$00$ P$.$M$.).$ All gensets except the main generator are shut down at $10$:$00$ P$.$M$.$ Forecasts indicate the need for $3,200$ megawatts more than provided by the main generator before $2$:$00$ P$.$M$.,$ and this need goes up to $5,700$ megawatts between $2$:$00$ and $10$:$00$ P$.$M$.$ Genset $1$ may provide up to $2,400$ megawatts, genset $2$ may provide up to $2,100$ megawatts, and genset $3$ may provide up to $3,300$ megawatts. The cost per megawatt used per eight$-$hour period is $$8$ for $1,$$$9$ for $2,$ and $$7$ for $3.$

Formulate this problem as an integer programming problem to determine the least$-$cost way to meet the needs of the area.

Problem #$2$