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Question 1 Kako king has won a lucrative school feeding program to supply breakfast to all students of Acera Internal School (AIS). Each mcal must come from one of four basic food groups. At present, the company has the following four meals in its catalogues available for consumption: Oats, Hausa Koko, Tom Brown and Rice Porridge. Koko King can eam a profit of GHC 0.50 for each pack of Oat meal. Hausa Koko provides GHC 0.20 profit per pack, whiles Tom Brown and Rice Porridge generate GHC 0.30, and GHC 0.80 profits per pack respectively. Each day, students must ingest at most 50.000 calories, 600 oz of chocolate paste, 1000 oz of sugar and 800 oz of fat. Strict nutritional guidelines must be met in order to sustain the contract. Nutritional experts at Koko King believe that cach pack of Oat meal provides 200 calories, 3 ounces of chocolate, and 2 ounces each of sugar and fat. Hausa Koko provides 2 ounces of chocolate paste and just as much calories as that provides by Oat meal. A pack of Tom Brown and Rice Porridge contains no chocolate paste, but Tom Brown provides 150 calories, 4 ounces of sugar and an ounce of fat. Finally, Rice Porridges 250 calories, 4 ounces of sugar and 5 ounces of fat per pack. Koko King want to know how many packs of each meal to serve in order to maximize profits a) i. Formulate a linear programming model that can be used to satisfy the daily nutritional requirements at a maximum profit. ii. Convert the Linear Programming model to the standard form CR (10 marks) The formulated in (a) was solved using Solver and the sensitivity report is given below Adjustable Cells Cell SCS2 SDS2 SES2 SFS2 Name Oat Hausa Koko Tom Brown Rice Porridge Final Value 100 0 0 120 Reduced Cost 0 -0.44 -0.04 0 Objective Coefficient 0.5 0.2 0.3 0.8 Allowable Increase 0.14 0.44 0.04 0.2 Allowable Decrease 0.04 1E30 1E+30 0.175 Constraints Cell Name SGS4 Calories SGSS Chocolate SGS6 Sugar SGS7 Fat Final Value 50000 300 680 800 Shadow Price 0.0018 0 0 0.07 Constraint Allowable R.H. Side Increase 50000 10000 600 IE-30 1000 1E+30 800 200 Allowable Decrease 10000 300 320 200 b) i. Determine the total daily profit of Koko King, ii. If Koko King increases the per unit profit of Rice Porridge to GHC 0,9, what will be the effect on the optimal solution and the total profit EV (10 marks) 2

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