Engineering Optimization
ISYE3133C
Homework assignment # 3:
Due Monday Mach 31st at the beginning of the class, which means
electronic submission will be automatically closed at 10:05AM and you should hand in the
handwritten part at the beginning of the class. If you turn the first 3 questions of your Homework
by Friday March 28
st
at the beginning of the class (and submit your files before 10:05AM the
same day) and you obtain at least 85/100 (without considering the extra credit question) you will
get 5 extra credit points in Midterm 2.
•
Remember that you are allowed to work with others, just let me know who you worked
with.
1.Junkfood Diet
Consider the small diet problem that we have seen in class before:
My diet requires that all the food I eat come from one or more of the four “basic food
groups” (chocolate cake, ice cream, soda, and cheesecake).
At present, the following four
foods are available for consumption: brownies, chocolate ice cream, cola, and pineapple
cheesecake.
Each brownie costs 50 cents, each scoop of chocolate ice cream costs 20
cents, each bottle of cola costs 30 cents, and each piece of pineapple cheesecake costs 80
cents.
Each day, I must ingest at least 500 calories, 6 oz of chocolate, 10 oz of sugar, and
8 oz of fat.
The nutritional content per unit of each food is shown in the table below.
Formulate a linear programming model that can be used to satisfy my daily nutritional
requirements at minimum cost.
Calories
Chocolate (oz)
Sugar (oz)
Fat (oz)
Brownie
400
3
2
2
Chocolate ice
cream (scoop)
200
2
2
4
Cola (bottle)
150
0
4
1
Pineapple
cheesecake
(piece)
500
0
4
5
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View Full DocumentBelow is the LINDO formulation for the problem:
MIN
50 BR + 20 IC + 30 COLA + 80 PC
SUBJECT TO
CAL)
400 BR + 200 IC + 150 COLA + 500 PC >=
500
CHOC)
3 BR + 2 IC >=
6
SUG)
2 BR + 2 IC + 4 COLA + 4 PC >=
10
FAT)
2 BR + 4 IC + COLA + 5 PC >=
8
END
Solve the problem with LINDO and answer the following questions.
Justify each answer with
information from the LINDO output.
Note: Make sure to answer YES to “Do range(sensitivity) analysis?” when you solve the
problem. The values of the dual optimal solution show up as dual prices in the LINDO output
and they might have the opposite sign.
Also remember that LINDO will internally transform the problem to standard form, hence the
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 Spring '08
 JuanPabloVielma
 Linear Programming, Optimization, Mathematical optimization, optimal solution, Shadow price, LINDO

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