JUNK FOOD OR GENUINE NOURISHMENT : THE NUTRITIONAL VALUE OF SOME SOUTH AFRICAN FAST-FOOD CHAINS

RC VAN DEN HONERT Department of Statistical Sciences University of Cape Town Rondebosch 7700 South Africa Integer programming is used to test the nutritional completeness of two fast-food chains operating in South Africa, McDonald's and Kentucky Fried Chicken. lt is shown that a fully nutritional and varied daily diet can be made up from McDonald's menu items, but the same is not true for Kentucky Fried Chicken. This exercise is highly suited to introduce students to mathematical programming: skills learned include formulating mathematical programming problems, mastering linear programming software and exploring the Internet for relevant data.


INTRODUCTION
Fast-food restaurants are usually considered to be "junk food" restaurants, and to be avoided if one is serious about the nutritional content of one's diet.But how true is this?The world's most famous fast-food chain, McDonald's, has recently located into South Africa, and we set out to answer the question: is it possible to construct a daily diet which was nutritionally complete (in the dietary sense) and comprised only of items from the McDonald's South African menu?If this was so, what combinations of menu items would together constitute a nutritionally complete diet (i.e. could be considered "wholesome")?And how much would such a daily diet cost the consumer?A natural extension of this would be to compare the cost of a nutritionally complete diet across various fast-food chains.
The diet problem was one of the first linear optimisation problems to be studied bar:k in the 1930s and 1940s.lt was motivated during the World War 11 by the US 1\nny' ~; http://orion.journals.ac.za/ desire to meet the nutritional requirements of the field Gls at minimum cost.On0 of the early researchers to formally study this problem was George Stigler. In 1945 Stigler formulated a diet problem as a linear programming (LP) problem in which 77 food types were available (including wheat flour, cabbage, spinach, corn meal, evaporated milk, peanut butter and pork liver) and 1 0 nutritional requirements (vitamin A, vitamin C, and so on) had to be satisfied (see Stigler, 1945).Since Oantzig's simplex solution to the LP problem only appeared in 1947, Stigler had to resort to a heuristic approach to solve this problem.The optimal heuristic result had an estimated cost of $39.93 per year (1939 prices).In the fall of 1947, Jack Laderman of the Mathematical T abies Project of the National Bureau of Standards undertook solving Stigler's model with Oantzig's new simplex method.1t was the first "large scale" computation in linear optimisation.The LP consisted of nine equations in 77 unknowns, and it took nine clerks using hand-operated desk calculators 120 man-days to solve for the optimal solution.The cost of the optimal diet was $39.69 per year -not far off Stigler's heuristic solution.The optimal "computer'' solution yielded a rather bland diet, consisting of the items mentioned above, which would probably not meet a minimum standard of tastiness (Stigler required that the same diet be eaten each day)."Tastiness" was clearly not included in the model formulation.Bosch (1993Bosch ( , 1995) ) revisited the diet problem, constructing nutritionally complete daily diets (in much the same way as Stigler did) for McDonald's, Wendy's and Burger King (the three largest hamburger chains in the US), and comparing them on a cost basis.Of the three chains, only McDonald's is represented in South Africa, and even then the menu has been adapted to suit local demand.Furthermore, the pricing structure of menu items appears to be completely different to the US menu, so a look at the McDonald's diet problem from a South African perspective is interesting.A comparison with a competing (non-hamburger) fast-food outlet offers insight into value -for money amongst fast food vendors (where value for money is defined in terms of nutritional value offered per rand spent).For the purposes of this study the consumer was assumed to be a male, aged between 19 and 24 years, weighing 72 kg and 1. 77 metres tall, and then the daily dietary requirements were such that this consumer had to obtain • less than 30% of his total energy (calories) from fat • less than 10% of his total energy from saturated fats • between 55% and 60% of his total energy from carbohydrates (Note that 1 g of fat= 9 calories, and 1 g of carbohydrates = 4 calories).
Furthermore the daily diet had to provide • less than 300mg of cholesterol • between 120mg and 2400mg of sodium • at least 58g of protein • between 2200 and 2600 calories.
A further goal in determining •an optimal daily diet is that it should be divided into two interesting meals (lunch and dinner), each with a main meal and a beverage (this step was clearly omitted by Stigler!).Thus for this study it was assumed that a typical fast-food patron would find a daily diet "reasonable" if it contains • at least two main meals, different from one another (to provide variety) • exactly two beverages Furthermore, constraints were added that ensured that the main meal at McDonald's was supplemented by at least one side dish -either chips or a dessert.(The reader may wish to add to this list of constraints, or reduce it).lt should be stressed here Several assumptions and approximations had to be made.Certain items on the South African menus were not contained in the official nutritional data, and so were omitted from the study altogether unless additional nutritional information could be obtained from alternative sources (e.g.beverage manufacturers}.Furthermore serving sizes/quantities of some items on the SA menus were different to the official US serving sizes/quantities.In this case local nutritional values had to be calculated in the correct proportions based on the US data.In the case of KBntucky Fried Chicken, individual pieces consist of either a whole wing, a bwasl, n drumstick or a thigh.For meals that consist of a combination of proc::os ( ft q ; 1 "I 1vnr" contains an http://orion.journals.ac.za/ assortment of 5 pieces) an average nutritional content was calculated assuming an equal amount of wing, breast, drumstick and thigh.Furthermore, menus change from time to time; the data for this study is relevant to menus as at October 1997.
The integer programming formulation for the McDonald's diet problem can be found in Appendix 3. A similar formulation can be derived for the Kentucky Fried Chicken (KFC) diet problem.The problem was solved using UNDO software.

RESULTS • BASIC DIETS
The optimal (cheapest) daily diet at McDonald's that satisfies all the nutritional and reasonableness requirements is given in Table 1.The daily diet in Table 2 appears to contain an excessive quantity of chips; these were obviously included in this solution to increase the caloric count.Even after allowing for the violation of the fat constraint, the KFC daily diet is vastly more expensive than the McDonald's daily diet (R38-16 compared to R25-00), making it clear that McDonald's offers better nutritional value for money than does KFC.Other near-optimal KFC solutions (violating the proportion of fat constraint and the total calorie count) are shown in Table 3  lt is seen that the effect of forcing two chicken meals into the optimal McDonald's daily diet results in a price increase of 22.4% over the basic optimal diet, implying that chicken in a fast-food menu is a more expensive component than ground beef or fish.However the McDonald's two-chicken-meals diet is still significantly cheaper than the best near-optimal KFC diet (R30-60 versus R38-16) .

RESULTS -OTHER DIETS
Since the KFC di~t is "nutritionally incomplete", it was excluded from further study and discussion here.Whilst the optimal McDonald's diet presented in Table 1 is nutritionally complete and reasonnhlo, it r:otJid bo dnscribAd by patrons at McDonald's as somewhat boring.After all, as far as llm main moals are concerned it contains only the standard hamburger and IIlo I 1iul 0 I ISIL I o satisfy customers http://orion.journals.ac.za/ who might be unhappy with the Table 1 diet, the mathematical model that was used to obtain the Table 1 diets were repeatedly modified, once for each main meal missing from Table 1.Each time the goal was to force a particular main meal into the diet, achieved by adding a single constraint to the basic mathematical modeL The resulting diets are listed in Table 5.
The entries in the "Extra Cost" column of Table 5 indicate the extra cost to the consumer for those diets over and above the basic optimal McDonald's diet.
(Alternatively, these costs can be interpreted as the amount by which McDonald's would have to reduce the cost of each main meal to have it included in the basic optimal diet).Thirdly, it highlights the point that the input data for most OR problems is not always easily available, and needs to be actively sought out.Students are encouraged to go and visit the problem-area (and to sample the vendor's wares while they are about it, if they wish!).Almost all students today have access to the Internet to find the required nutritional information (I give students this hint after a few days if they have not worked it out yet); thus a further spin-off of a project of this nature is that it often presents students with their first opportunity to constructively "surf the net".Thus students learn a variety of techniques and tools in a single aggregated setting.Furthermore this setting is not restricted to the fast-food chains mentioned here: many products on supermarket shelves offer nutritional information on their http://orion.journals.ac.za/ packaging, and the problem could easily be adapted to construct optimal daily diets from a given set of products, using suitable constraints.

Table 1 .
Bosch (1995)y diet for McDonald'sBosch (1995)had an optimal McDonald's daily diet consisting of two hamburgers, a small McFries, a side salad with croutons and a lite dressing, a small orange juice and a small vanilla milkshake.ltshouldbe noted here that the South African McDor tald's outlets do not serve salads (and a lot of other US menu items), and relatively high total fat content, or were relatively low in caloric value.A near-optimal diet from KFC, which only violated the maximum percentage from fat constraint is shown in Table2.
A feasible diet satisfying all the nutritional requirements was not possible for KFC.On closer examination of the data it was evident that menu items at KFC had a http://orion.journals.ac.za/

Table 2 .
Near-Optimal daily diet for Kentucky Fried Chicken

Table 3 .
Other Near-Optimal daily diets for Kentucky Fried Chicken (at least 1600, 1800 and 2000 Calories) both ground beef and fish, but not chicken).To avoid this bias the McDonald's problem was re-solved after adding constraints to ensure that chicken was included in one, and then both, meals.The results of this exercise are found in Table4.

Table 4 .
Optimal daily diets for McDonald's (one and two chicken meals)

Table 5 .
Optimal daily diets that include particular McDonald's main meals lt is interesting to note that only one main meal -McNuggets 20 Pieces -could not be included in an optimal diet.The McNuggets 20 Pieces is essentially a family meal, meant for more than one person, and its size ensures that it has high cholesterol and sodium levels.When the model was adapted to allow a singleMcNuggets 20 Pieces to be considered as both the day's main meals in one, it too can be included in an optimal diet.The above analyses make it abundantly clear that the McDonald's menu indeed offers wholesome and nutritious meals at a reasonable cost.Advantages of this problem and this approach if used as a class project are several.Firstly, the problem is bigger (in terms of the number of variables and constraints) than most encountered in the typical classroom text book, so ensuring that students get the idea that in practice not all LP problems have 3 variables and 2 constraints, and can all be solved by hand graphically or by using the simplex http://orion.journals.ac.za/ technique by 11and!Thus the student will have to be exposed to LP software to reach a solution.I have chosen the UNDO software here as the student version comes supplied with some modem textbooks in operational research/management science (and indeed the one that I typically use for the course).This package is extremely quick and easy to install and use, and is very user friendly.Furthermore the full commercial version of UNDO is one of the most widely-available and -used commercial LP software.Secondly, the setting is interesting to most students, who inevitably would have been exposed to the fast-food way of eating.This level of interest is often converted into an increased dedication to exploring the problem.