FYV not exactly the smartest option one would

Solutions Manual for Operations Research, An Introduction, 11e Hamdy Taha (All Chapters Download link at the end of this file) 1 / 2

Chapter 1 1 Buy five 1-way FYV-DEN and five 1-way DEN- FYV (not exactly the smartest option one would consider, but it is feasible).Cost = 10x(.75x400) = $3000 2 Width, x Height, h Area 10 20 30 40 40 30 20 10 400 600 600 400 No, the calculations only indicate that the maximum appears to lie between x=20 and x=30. In general, functions may have local maxima, which may be detected conveniently in this one-dimensional case by graphing the function, an unnecessary time-consuming task. What is needed is a method that can locate the maximum, in the present example with calculus.3

co

continued…

A1 A2 A3

A0 A4

• cont’d

Height of the (shaded) rectangle is x units shorter than L.Base of rectangle is x units longer than L. Thus, A3 is square with side x. Construct A2, a mirror image of A3. Hence, area A1 = area A4.Area of square of side L = A0 + A1 + A2 Area of rectangle = A0 + A4 = A0 + A1.

Conclusion: Area of square is larger than area of

rectangle by A2 (= x 2 ).

Algebraic solution: For 0 < x < L, the square area L

2

is larger than the rectangle area of (L + x) (L – x) = L 2

• x

2 , which is the same result shown by the graph.4

• 2 2

2 5 8

• 5Circle circumference
• 16Square perimiter

Per triangle: ( ) ( )

Hence square perimiter is larger 1 a a r a r a r r



= + −

=  ==

L x L 1-2 .

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