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Problem 2. (4 points): Write the dual program of the following linear programming problem.
No need to solve the dual nor the primal.
Minimize z = 7561 + 61:2 4223
St 3m + 8x2 5:133 2 14
x1 2:112 + 9.13 = 17
2:121 + 3:122 < 19 => '2X.3Y1E'
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Problem 2. (6 points): For any real number m, let fm be the function dened by
fm(:c, y) = m2 + my2 + 2m.
In function of m, nd the stationary points of fm and determine their nature (saddle point, local
minimum or local maximum).
m mm lml
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Problem 4. (8 points): In your 100-acre farm, you are planning to grow tomatoes, lettuce, and
carrots in the coming planting season. Fertilizer costs per acre : $5 for tomatoes, $4 for lettuce,
and $2 for carrots. Based on past exper
, OPTIMIZE : max 0/ mm
- Vaables xHxZ/Wyp CCU/6C! DECISION VARIABLES
r Smear) 70 a om Lad/w: FUNCTION
7* ALL OdvLa sahsgrg CmsMkhw+5 / nap/15mg
T. 54:}? mp *Eémie sp/Lcnm W FQJI'PLE
(Could be em;y> '_ _
smalles+ or kaiyesf WI/ac of olecrt 7mJ = OWWAL
VA
Nabil Kahouadji, Ph.D.
Math 368, Winter 2016
Mathematics Department
Introduction to Optimization
Math 368: Syllabus
Instructor and Teaching Assistant Contact Information
Role
Name
Contact
Phone/Fax:
Oce:
E-mail:
Instructor
Nabil Kahouadji
Webpage:
Oce Hou