OPERATIONS MANAGEMENT
Posted: Sat Feb 19, 2022 3:05 pm
OPERATIONS MANAGEMENT
Question 3 [12] A South African university would like to open a mini-restaurant with free food for its students. The choice of menu was decided after short interviews with a few students. It was decided to purchase the following food items: Food item Cost (in rand) R40 R4 R60 Fried rice (100 g) Bread (1 slice) Beef burger (100 g) Fried fish (100 g) Orange juice (1 glass) Iced tea with milk (1 glass) Water (500 ml bottle) R50 R15 R12 R10 The head of the restaurant only considers four nutrients, namely protein, fat, calcium and vitamin C. The recommended daily intake for each student is set as follows: Protein: between 48 and 80 grams (g) - Fat: at most 66 grams Vitamin C: between 65 and 90 milligram (mg) The nutritional content of each food item is given in the following table:
Food item Protein Fat (g) Calcium (mg) Vitamin C (mg) 4.7 2.3 14 0 1.1 0.4 23.4 0 21 12 17 0 Fried rice (100 g) Bread (1 slice) Beef burger (100 g) Fried fish (100 g) Orange juice (1 glass) Iced tea with milk (1 glass) Water (500 ml bottle) 22 0 20 0 0.7 0.2 11 50 1.4 1 125 2.5 0 0 2 0 For practical reasons, each student will need at most four (4) slices of bread and exactly one (1) glass of liquid (orange juice, iced tea with milk and/or water). In addition, the ratio of vitamin C to calcium in the meal served should not exceed 0.05. The management of the restaurant would like to select a food choice for each student that minimises the total cost while meeting all requirements. (a) Define all the decision variables of the problem clearly. (b) Formulate the objective function that minimises the total cost. (c) Formulate all functional constraints. (2) (2) (8)
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Food item Protein Fat (g) Calcium (mg) Vitamin C (mg) 4.7 2.3 14 0 1.1 0.4 23.4 0 21 12 17 0 Fried rice (100 g) Bread (1 slice) Beef burger (100 g) Fried fish (100 g) Orange juice (1 glass) Iced tea with milk (1 glass) Water (500 ml bottle) 22 0 20 0 0.7 0.2 11 50 1.4 1 125 2.5 0 0 2 0 For practical reasons, each student will need at most four (4) slices of bread and exactly one (1) glass of liquid (orange juice, iced tea with milk and/or water). In addition, the ratio of vitamin C to calcium in the meal served should not exceed 0.05. The management of the restaurant would like to select a food choice for each student that minimises the total cost while meeting all requirements. (a) Define all the decision variables of the problem clearly. (b) Formulate the objective function that minimises the total cost. (c) Formulate all functional constraints. (2) (2) (8)