Nonlinear Programming

• It is easy to use the Excel Solver to solve NLPs.
• The process is similar to a linear model.
• For NLPs having multiple local optimal solutions, the Solver may fail to find the optimal solution because it may pick a local extremum that is not a global extremum.

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Example 2
• Trucko is trying to determine where they should locate a single warehouse. The positions in the x‐y plane of their four customers and the number of shipments made annually to each customer are given. Trucko wants to locate the warehouse to minimize the total distance trucks must travel annually from the warehouse to the four customers.
Customer

X‐coordinate

Y‐coordinate

Number of
Shipments

1

5

10

200

2

10

5

150

3

0

12

200

4

12

0

300
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1

Example 3
• Q& H Company advertises on soap operas and football games. Each soap opera ad costs $50000, and each football game ad costs $10000. Giving all figures in millions of viewers, S soap opera ads are bought, they will be seen by
5S men and 20 S women. If F football Ads are bought they will be seen by 17F men and 7F women. Q&H wants at least40 million men and at least 60 million women to see its ads.
• Formulate the NLP
• Suppose the number of women reached by F football ads and S soap opera ads is 7F+ 20 S ‐0.2 (FS). Why might this be a more realistic representation of the number of women viewers seeing Q&H’s ads?
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Example 3: cont’d
• Let S = soap opera ads and
F = football ads. Then we wish to min z = 50S + 100F st 5S1/2 + 17F1/240 (men)
20S1/2 + 7F1/260 (women)
S0, F0

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2

Review of Differential Calculus
• The equation

lim f ( x)  c x a

means that as x gets closer to a (but not equal to
a), the value of f(x) gets arbitrarily close to c.
• A function f(x) is continuous at a point if lim f ( x)  f (a ) xa If f(x) is not continuous at x=a, we say that f(x) is
discontinuous