Engineering Optimization: Theory and Practice, Fourth Edition

174 Linear Programming I: Simplex Method

3.97 A bank offers four different types of certificates of deposits (CDs) as indicated below:

CD type Duration (yr) Total interest at maturity (%)

1 0.5 5

2 1.0 7

3 2.0 10

4 4.0 15

If a customer wants to invest $50,000 in various types of CDs, determine the plan that

yields the maximum return at the end of the fourth year.

3.98 The production of two machine partsAandBrequires operations on a lathe(L), a

shaper(S), a drilling machine(D), a milling machine(M), and a grinding machine

(G). The machining times required byAandBon various machines are given below.

Machine time required (hours per unit) on:

Machine part L S D M G

A 0.6 0.4 0.1 0.5 0.2

B 0.9 0.1 0.2 0.3 0.3

The number of machines of different types available is given byL: 10, S: 3, D: 4, M:

6, andG: 5. Each machine can be used for 8 hours a day for 30 days in a month.

(a)Determine the production plan for maximizing the output in a month

(b)If the number of units ofAis to be equal to the number of units ofB, find the

optimum production plan.

3.99 A salesman sells two types of vacuum cleaners,AandB. He receives a commission of

20% on all sales, provided that at least 10 units each ofAandBare sold per month.

The salesman needs to make telephone calls to make appointments with customers and

demonstrate the products in order to sell the products. The selling price of the products,

the average money to be spent on telephone calls, the time to be spent on demonstrations,

and the probability of a potential customer buying the product are given below:

Vacuum

cleaner

Selling

price per

unit

Money to be spent on

telephone calls to find

a potential customer

Time to be spent in

demonstrations to a

potential customer (hr)

Probability of a

potential customer

buying the product

A $250 $3 3 0.4

B $100 $1 1 0.8

In a particular month, the salesman expects to sell at most 25 units ofAand 45 units of

B. If he plans to spend a maximum of 200 hours in the month, formulate the problem

of determining the number of units ofAandBto be sold to maximize his income.

3.100 An electric utility company operates two thermal power plants,AandB, using three

different grades of coal,C 1 ,C 2 , andC 3. The minimum power to be generated at plantsA

andBis 30 and 80 MWh, respectively. The quantities of various grades of coal required

to generate 1 MWh of power at each power plant, the pollution caused by the various

grades of coal at each power plant, and the costs of coal are given in the following table: