ISYE 3133 Homerwork3sol

ISYE 3133 Homerwork3sol - Engineering Optimization...

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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.Junk-food 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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Below 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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ISYE 3133 Homerwork3sol - Engineering Optimization...

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