Engineering Optimization: Theory and Practice, Fourth Edition

172 Linear Programming I: Simplex Method

3.85 Problem 3.38

3.86 Problem 3.39

3.87 Problem 3.40

3.88 Problem 3.41

3.89 Problem 3.42

3.90 Problem 3.43

3.91 The temperatures measured at various points inside a heated wall are given below:

Distance from the heated surface as a

percentage of wall thickness,xi 0 20 40 60 80 100

Temperature,ti(◦C) 400 350 250 175 100 50

It is decided to use a linear model to approximate the measured values as

t=a+bx (1)

wheretis the temperature,xthe percentage of wall thickness, andaandbthe coefficients

that are to be estimated. Obtain the best estimates ofaandbusing linear programming

with the following objectives.

(a)Minimize the sum of absolute deviations between the measured values and those

given by Eq. (1):i|a+bxi−ti|.

(b)Minimize the maximum absolute deviation between the measured values and those

given by Eq. (1):

Max

i

|a+bxi−ti|

3.92 A snack food manufacturer markets two kinds of mixed nuts, labeledAandB. Mixed

nutsAcontain 20% almonds, 10% cashew nuts, 15% walnuts, and 55% peanuts. Mixed

nutsBcontain 10% almonds, 20% cashew nuts, 25% walnuts, and 45% peanuts. A

customer wants to use mixed nutsAandBto prepare a new mix that contains at least

4 lb of almonds, 5 lb of cashew nuts, and 6 lb of walnuts, for a party. If mixed nutsA

andBcost $2.50 and $3.00 per pound, respectively, determine the amounts of mixed

nutsAandBto be used to prepare the new mix at a minimum cost.

3.93 A company produces three types of bearings,B 1 ,B 2 , andB 3 , on two machines,A 1

andA 2. The processing times of the bearings on the two machines are indicated in the

following table:

Processing time (min) for bearing:

Machine B 1 B 2 B 3

A 1 10 6 12

A 2 8 4 4