Engineering Optimization: Theory and Practice, Fourth Edition

52 Introduction to Optimization

Figure 1.20 Shell-and-tube heat exchanger.

Figure 1.21 Electrical bridge network.

1.13 The bridge network shown in Fig. 1.21 consists of five resistorsRi(i= 1 , 2 ,... , 5 ).

IfIiis the current flowing through the resistanceRi, the problem is to find the resistances

R 1 , R 2 ,... , R 5 so that the total power dissipated by the network is a minimum. The

currentIican vary between the lower and upper limitsIi,minandIi,max, and the voltage

drop,Vi=RiIi, must be equal to a constantcifor 1≤i≤5. Formulate the problem as

a mathematical programming problem.

1.14 A traveling saleswoman has to coverntowns. She plans to start from a particular town

numbered 1, visit each of the othern−1 towns, and return to the town 1. The distance

between townsiandjis given bydij. Formulate the problem of selecting the sequence

in which the towns are to be visited to minimize the total distance traveled.

1.15 A farmer has a choice of planting barley, oats, rice, or wheat on his 200-acre farm. The

labor, water, and fertilizer requirements, yields per acre, and selling prices are given in

the following table:

Labor Water Fertilizer Selling

Type of cost required required Yield price

crop ($) (m^3 ) (lb) (lb) ($/lb)

Barley 300 10,000 100 1,500 0.5

Oats 200 7,000 120 3,000 0.2

Rice 250 6,000 160 2,500 0.3

Wheat 360 8,000 200 2,000 0.4

The farmer can also give part or all of the land for lease, in which case he gets $200 per

acre. The cost of water is $0.02/m^3 and the cost of the fertilizer is $2/lb. Assume that

the farmer has no money to start with and can get a maximum loan of $50,000 from the

land mortgage bank at an interest of 8 %. He can repay the loan after six months. The