This is a problem from Wayne Winston’s Operations Research, 3rd Edition:

City 1 produces 500 tons of waste per day and city 2 produces 400 tons of waste per day. Waste must be incinerated at incinerator 1 or 2, and each incinerator can process up to 500 tons of waste per day. The cost to incinerate waste is $40/ton at incinerator 1 and $30/ton at 2. Incineration reduces each ton of waste to 0.2 tons of debris, which must be dumped at one of two landfills. Each landfill can receive at most 200 tons of debris per day. It costs $3 per mile to transport a ton of debris (either debris or waste). Distance (in miles) between locations are shown in the table below:

Incinerator 1 Incinerator 2City 1 30 5City 2 36 42

Landfill 1 Landfill 2Incinerator 1 5 8Incinerator 2 9 6

Minimize the total cost of disposing of the waste of both cities.

/* SAS Code for solving this LP */

Options nodate;

Data;

Input _id_ $ w11 w12 w21 w22 d11 d12 d21 d22 _type_$ _rhs_;

Cards;

Cost 130 45 148 156 5 24 27 18 min .

city1 1 1 0 0 0 0 0 0 eq 500

city2 0 0 1 1 0 0 0 0 eq 400

incen1 1 0 1 0 0 0 0 0 le 500

incen2 0 1 0 1 0 0 0 0 le 500

deb-1 0 0 0 0 1 0 1 0 le 200

deb-2 0 0 0 0 0 1 0 1 le 200

w1-d1 -0.2 0 -0.2 0 1 1 0 0 eq 0

w2=d2 0 -0.2 0 -0.2 0 0 1 1 eq 0

;

proc lp rangeprice rangerhs;

run;