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THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
MATH3161 OPTIMIZATION Term 1, 2021
ASSIGNMENT
Your answers to this assignment must be submitted via Moodle before 5:00pm, April
23, 2021. Late assignments will not be accepted except on documented medical or compassionate
grounds.
Assignments must include a signed cover sheet available from the School of Mathematics and
Statistics web site at:
School date stamp is not needed on the cover sheet .
Marking of this Assignment
Each question on this assignment is worth 25 marks. A full mark of 50 on this as-
signment is worth 5% of the total marks for MATH3161. Present your work as a self
contained, well-written report including the problem statement, solution summary, clear
interpretation of solutions, model formulation, definition of problem variables and your
computer output. State clearly the assumptions that you make. Any Matlab files that
you modify/write should be included as an appendix.
1. Minimum Cost Pizza Problem. Using only the items given in the tables below, formulate
an optimization problem in standard form to create a minimum cost pizza which satisfies both the
nutritional requirements of Table 1 and bounds on item quantities given in Table 2. Use the nutritional
data of Table 3 and the cost data of Table 4 in your model.
Use the MATLAB linear optimization routines linprog to solve the problem. Interpret your results.
Table 1
Nutrient Requirement Units
Calcium 750.0 mg
Iron 12.0 mg
Protein 48.5 gram
Vitamin A 4500.0 IU
Thiamine 1.3 mg
Niacin 16.0 mg
Riboflavin 1.6 mg
Vitamin C 30.0 mg
1
Table 2
UPPER AND LOWER BOUNDS ON PIZZA ITEMS
Item Upper Bounds* Lower Bound*
Sauce 1.986 1.140
dough 5.249 4.266
cheese 2.270 1.703
pepperoni 0.983 N/A
ham 1.135 N/A
bacon 0.993 N/A
g.pepper 1.561 N/A
onion 0.993 N/A
celery 1.561 N/A
mushroom 1.135 N/A
tomato 1.703 N/A
pineapple 1.703 N/A
meat N/A 0.993
veg. N/A 0.993
fungi N/A 0.922
* Amount in hundreds of grams.
Table 3
NUTRITIONAL DECOMPOSITION OF PIZZA ITEMS*
Item Calc Iron Prot Vit A Thia Niac Ribo Vit C
cheese 517.700 .222 20.000 3000.000 .022 6.000 .244 -
Sauce 14.000 1.800 2.000 800.000 0.100 1.400 .060 6.000
dough 18.233 3.826 14.224 - .586 8.852 .628 -
pepperoni 10.000 2.500 15.000 - - 2.000 - -
ham 9.031 2.291 14.692 - .740 4.009 0.178 -
bacon 13.000 1.189 8.392 - .361 1.828 .114 -
g.pepper 9.459 .675 1.351 209.460 .081 .540 .081 127.030
onion 27.273 .545 1.818 18.182 .363 .545 .036 10.000
celery 40.000 .250 - 125.000 .025 .500 .025 10.000
mushroom 6.000 .800 3.000 - .100 4.300 .460 3.000
tomato 13.333 .533 1.333 450.000 .066 .800 .04 22.667
pineapple 12.016 .310 .387 25.194 .081 .193 .019 6.977
* Units as in Table 1