Engineering Optimization: Theory and Practice, Fourth Edition

Problems 175

Quantity of coal
required to generate 1 Pollution Cost of coal
MWh at the power caused at at power
plant (tons) power plant plant
Coal type A B A B A B

C 1 2.5 1.5 1.0 1.5 20 18

C 2 1.0 2.0 1.5 2.0 25 28

C 3 3.0 2.5 2.0 2.5 18 12

Formulate the problem of determining the amounts of different grades of coal to be used

at each power plant to minimize (a) the total pollution level, and (b) the total cost of

operation.

3.101 A grocery store wants to buy five different types of vegetables from four farms in a
month. The prices of the vegetables at different farms, the capacities of the farms, and
the minimum requirements of the grocery store are indicated in the following table:

Price ($/ton) of vegetable type Maximum (of all

1 2 3 4 5 types combined)

Farm (Potato) (Tomato) (Okra) (Eggplant) (Spinach) they can supply

1 200 600 1600 800 1200 180

2 300 550 1400 850 1100 200

3 250 650 1500 700 1000 100

4 150 500 1700 900 1300 120

Minimum amount

required (tons) 100 60 20 80 40

Formulate the problem of determining the buying scheme that corresponds to a

minimum cost.

3.102 A steel plant produces steel using four different types of processes. The iron ore, coal,
and labor required, the amounts of steel and side products produced, the cost information,
and the physical limitations on the system are given below:

Side
Iron ore Coal Steel products
required required Labor required Produced Produced
Process type (tons/day) (tons/day) (person-days) (tons/day) (tons/day)
1 5 3 6 4 1
2 8 5 12 6 2
3 3 2 5 2 1
4 10 7 12 6 4
Cost $50/ton $10/ton $150/person-day $350/ton $100/ton

Limitations 600 tons
available
per
month

250 tons

available

per

month

No limita-

tions on

availability

of labor

All steel

produced

can be

sold

Only 200

tons can

be sold

per month