**Article 1** **Least Cost Diet for Children Two to Three Years in Malaysia Using Linear Programming Approach** Nor Hayati Shafii\*, Rohana Alias, Noradilla Radzuan Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Malaysia , , *Abstract* *The early period of life, namely from birth to two years of age is critical for the promotion of optimal growth, brain development as well as health and behavioural development. Thus, attaining the daily required nutrition during this stage of life is very crucial since nutrition is strongly associated with a child’s development at a very young age. It is a major challenge for Malaysians to ensure children get a* *balanced diet, especially children* *from families of low socioeconomic status. As reported in the Edge Weekly, the review found that 24.9% or nearly one in four children in Malaysia experienced moderate or severe food insecurity due to financial constraints.* *In this study, a linear programming diet model is used to determine* *an affordable cheapest food basket that satisfies* *the daily recommended nutritional requirements for children between two to three years old in Malaysia. POM-QM for Windows Version 5.2 by Howard J. Weiss is used. Initial finding shows that the* *average costs are* *RM2.69. This food basket consists of 474g of eggs, 55g of tofu, 29g of papaya, 5g of spinach and 201g of potato. With this food basket and estimated food expenditure, parents can save for 40% of their child’s daily food expenditure.* *Keywords:* *Food Items, Linear Programming Model, Low Cost, Nutrition, Optimization* **Introduction** Malnutrition is associated with about half of all child deaths worldwide (Eunice et al., 2014). Possible explanations for this as addressed by Schönfeldt et al. (2010) are inefficient education on healthy eating habits and lack of ability to gain the necessary education due to economic constraints. Socioeconomic background is the main factor for parents ability to buy food with sufficient nutrients or otherwise (“WHO Global Database on Child Growth and Malnutrition 14,” 2011). In Malaysia, the prevalence of underweight and stunting persist among young children from poor rural areas (Khor & Sharif, 2003). According to Temim et al. (2010), the problem could be addressed by initiating low cost changes in the health system that would make the entire sector more responsive to the targeted people’s requirements. Linear programming has been utilised in various applications involving diet related problems. Okubo et al., (2015) has used linear programming to determine the pattern of food intake in fulfilling the recommendation of nutrient by Dietary Reference Intake (DRIs). Numerous researches have been done with different purposes such as by Briend et al., (2008) and Van der Merwe et al., (2014). **LP Model Formulation** This study uses linear programming approach i.e Simplex Method to determine the minimum food budget that satisfies the nutritional requirements for Malaysian children aged two to three years old. The nutrient content was derived from SELF Nutrition Data of Standard Tables Food Composition at nutritiondata.self.com. The Malaysian Dietary Guidelines for Children and Adolescents Summary was used to obtain the caloric, nutrient requirements, and Malaysian favourite food items. The suggestion by Ministry of Health (2013) was used to identify the food items in the food basket. The collection of food prices was carried out at Giant Hypermarket Kangar on March 26, 2017, and the prices were normal prices without promotion or discount. Objective function: Minimise cost Z = \(\sum_{j = 1}^{15}{c_{j}X_{j}}\) where, \(X_{j}\) = The quantity (100g) of the food item *j*, \(c_{j}\) = The cost of (100g) of food item *j*. The food items are milk\(\left( X_{1} \right)\), yoghurt-plain\(\left( X_{2} \right)\), chicken\(\left( X_{3} \right)\), egg\(\left( X_{4} \right)\), mackerel\(\left( X_{5} \right)\), tofu\(\left( X_{6} \right)\), banana\(\left( X_{7} \right)\), papaya\(\left( X_{8} \right)\), carrot\(\left( X_{9} \right)\), spinach\(\left( X_{10} \right)\), white rice\(\left( X_{11} \right)\), white bread\(\left( X_{12} \right)\), potato\(\left( X_{13} \right)\), plain biscuits \(\left( X_{14} \right)\), and noodles\(\left( X_{15} \right)\). The above objective function is subjected to the constraints: \(\sum_{j = 1}^{15}{A_{\text{ij}}X_{\text{ij}} \geq B_{i}}\text{\ \ \ \ \ ;\ \ \ \ }X_{j} \geq 0\) where, \(A_{\text{ij}}\)= The amount of nutrient *i* in food item *j*, and \(B_{i}\) = Minimum daily requirement of nutrient *i*. The constraints are Carbohydrates (\(C_{x}H_{y}O_{z})\), calcium (Ca), iron (Fe), magnesium (Mg), phosphorus (P), potassium (K), sodium (Na), vitamin A (Vit.A), vitamin C (Vit.C), vitamin E (Vit.E), vitamin K (Vit.K), energy, protein, and fats (Refer to Table 1). Table 1: Price and Nutritional Content of 100 grams of Food Items ![](91-1--1-6-20181025_media/media/image1.PNG) Prior to using POM-QM software to obtain the optimal solution, the inequality constraints were converted to equality constraints. This was done by introducing the slack and artificial variables. Specifically, in this study all the constraints contain more than inequality (). For example, the energy constraint is shown in equation (1). \[\begin{pmatrix} 176X_{1} + 255X_{2} + 691X_{3} + 821X_{4} + 1097X_{5} + \\ 607X_{6} + 373X_{7} + 163X_{8} + 147X_{9} + 96.3X_{10} \\ + 544X_{11} + 1227X_{12} + 389X_{13} + 1528X_{14} + 1608X_{15} \geq 1000kJ \\ \end{pmatrix} \] Subtracting the surplus \(S_{1}\) and adding the artificial variables \(A_{1}\) in equation (1) results in equation (2). \[{607X_{6} + 373X_{7} + 163X_{8} + 147X_{9} + 96.3X_{10} }{+ 544X_{11} + 1227X_{12} + 389X_{13} + 1528X_{14} + }\] **Results and Discussion** Table 2, 3 and 4 show the linear programming results. The result shows that RM2.68 is the minimum amount that parents need to spend daily on food for children of two to three years old, to meet their necessary nutritional requirements. The food basket must consist of 4.69g of eggs, 0.53g of tofu, 0.05g of spinach, 1.86g of potato and 0.68g of noodle. Table 2: Optimal Solution of Food Basket | | Milk | Yogurt | Chicken | Egg | Mackerel | Tofu | Banana | Papaya | Carrot | Spinach | Rice | Bread | Potato | Biscuits | Noodles | RHS | | | -------- | ----- | ------ | ------- | ----------- | -------- | ----------- | ------ | ------ | ------ | --------- | ----- | ----- | ----------- | -------- | ----------- | --- | ---------- | | Minimize | .5 | .78 | .72 | .33 | .96 | .3 | .37 | .28 | .3 | 1.5 | .23 | .6 | .4 | 1.06 | .22 | | | | Energy | 176 | 255 | 691 | 821 | 1097 | 607 | 373 | 163 | 147 | 96.3 | 544 | 1227 | 389 | 1528 | 1608 | \>= | 1000 | | | 5.2 | 4.7 | 0 | .9 | 0 | 4.3 | 22.8 | 9.8 | 8.2 | 3.7 | 28.6 | 54.4 | 21.2 | 48.5 | 71.3 | \>= | 22 | | Fats | 1 | 3.3 | 3.6 | 15.3 | 17.8 | 8.7 | .3 | .1 | .1 | .3 | .2 | .4 | .1 | 16.5 | 4.4 | \>= | 5 | | Protein | 3.4 | 3.5 | 31 | 13.6 | 23.9 | 15.8 | 1.1 | .6 | .6 | 3 | 2.4 | 9 | 2.5 | 6.2 | 14.2 | \>= | 12 | | Vit. A | 58.8 | 29.7 | 6.3 | 218.7 | 54 | 49.8 | 19.2 | 328.2 | 4137 | 3144.3 | 0 | 0 | 3 | .6 | 18.6 | \>= | 300 | | Vit. C | 0 | .5 | 0 | 0 | .4 | .2 | 8.7 | 61.8 | 2.6 | 9.8 | 0 | 0 | 9.6 | 0 | 0 | \>= | 15 | | Vit E | 0 | .1 | .3 | 1.2 | 0 | 0 | .1 | .7 | 0 | 2.1 | 0 | .2 | 0 | 1.3 | .4 | \>= | 6 | | Vit. K | .1 | .2 | 2.8 | .3 | 0 | 0 | .5 | 2.6 | 9.4 | 494 | 0 | 3.4 | 2 | 4.1 | .5 | \>= | 30 | | Ca | 119 | 121 | 15 | 59 | 15 | 683 | 5 | 24 | 32 | 136 | 3 | 119 | 15 | 49 | 35 | \>= | 700 | | Fe | 0 | .1 | 1 | 2 | 1.6 | 2.7 | .3 | .1 | .9 | 3.6 | 1.5 | 3.3 | 1.1 | 3.3 | 4 | \>= | 7 | | Mg | 11 | 12 | 29 | 13 | 97 | 58 | 27 | 10 | 10 | 87 | 13 | 26 | 28 | 17 | 58 | \>= | 65 | | P | 95 | 95 | 228 | 208 | 278 | 190 | 22 | 5 | 28 | 56 | 37 | 103 | 70 | 430 | 241 | \>= | 380 | | K | 150 | 155 | 256 | 147 | 401 | 237 | 358 | 257 | 237 | 466 | 29 | 131 | 535 | 224 | 244 | \>= | 2000 | | Na | 44 | 46 | 74 | 204 | 83 | 14 | 1 | 3 | 78 | 70 | 0 | 592 | 10 | 1052 | 21 | \>= | 1000 | | Solution | **0** | **0** | **0** | **4.68722** | **0** | **.534497** | **0** | **0** | **0** | **.4966** | **0** | **0** | **1.86132** | **0** | **.677628** | | **2.6752** | If parents wish to add food items other than those suggested in the Model, they need to increase food expenditure that follows the value of the “Reduced” column shown in Table 3. For example, the consumption of 100 grams of milk and yoghurt will increase the costs by RM0.34 and RM0.61, respectively. Table 3: Optimal Values of Food Items ![](91-1--1-6-20181025_media/media/image4.PNG) | Table 4: (i) Constraints Ranging Result (ii) Optimal values of nutrient requirement for the model | | | ------------------------------------------------------------------------------------------------- | ---------------------------------------------- | | ![](91-1--1-6-20181025_media/media/image5.png) | ![](91-1--1-6-20181025_media/media/image6.png) | Table 4 shows that the value of surplus variable are as follows: \(S_{1} =\)4991.108, \(S_{2} =\)72.47541, \(S_{3} =\)74.54718, \(S_{4} =\) 74.61584, \(S_{5} =\) 926.0453, \(S_{6} =\) 3.462236, \(S_{7} =\) 0, \(S_{8} =\) 0, \(S_{9} =\) 0, \(S_{10} =\) 8.754319, \(S_{11} =\) 122.6744, \(S_{12} =\) 992.8777, \(S_{13} =\) 0, and \(S_{14} =\) 0. Vitamin E, vitamin K, calcium, potassium and sodium have zero value for surplus variable where the resources are fully utilised. Thus, these five nutrients are binding constraints. However, a unit increase in the right-hand side of any of these nutrients will not increase food expenditure significantly. Meanwhile, the constraints on the energy, carbohydrates, fats, protein, vitamin A, vitamin C, iron, magnesium and phosphorus are not binding in the Model since the value of the surplus is not zero. This indicates that there is an excess amount of resources which are utilised. Therefore, the “level” column as shown in Table 4 are new limitations for the constraints. These values are from the original values plus the surplus values for each constraint. **Conclusion and Recommendations** This study aimed to find the least cost food basket which satisfied nutritional requirements for children between two to three years old in Malaysia. The Simplex method used in this study was successful in providing a systematic tool for designing least cost nutritious food basket. The least cost diet model proposed was also significant for parents from low income households as it provides information on proper balance diet of their children with affordable food items. Furthermore, all the suggested food items such as eggs, tofu, papaya, spinach, potato and noodle are widely available in Malaysia. This study only considered children for low household income from the Malay ethnic in Malaysia; not for any other specific cultural groups or races. It would be interesting if future research works can consider the food consumption patterns of specific cultural groups or races such as Chinese, Indian or other races in Sabah and Sarawak. **References** [*Malaysian Journal of Nutrition*](https://www.researchgate.net/journal/1394-035X_Malaysian_Journal_of_Nutrition) Briend, A., Darmon, N., Ferguson, E., & Erhardt, J. G. (2008). 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