The Whole Food Nutrition Center uses three bulk grains, A, B, and C, to blend a...

 

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The Whole Food Nutrition Center uses three bulk grains, A, B, and C, to blend a natural cereal that it sells by the pound. The cost of each bulk grain is indicated in the table below, along with the units of four types of nutrient (Nutrient 1, 2, 3, and 4) that is contained in each pound of the grains. After consulting with the nutritionist, Whole Food has determined that each pound serving of the cereal should contain 24 units of Nutrient 1, 16 units of Nutrient 2, 8 units of Nutrient 3, and 3.4 units of Nutrient 4. Whole Food wishes to decide how to blend the three types of grain in order to minimize the total cost of each pound of the cereal. In other words, they wish to solve the following optimization: Minimize 33A + 47B + 38C Subject to: Nutrient 1. Nutrient 2 Nutrient 3 Nutrient 4 22A + 28B + 21C 24 16A + 14B + 25C 16 8A+7B +9C 28 5A A+ B + C =1 A,B,C 20 +66231 Cost per pound of grain (cents) Grain A 22 16 8 5 33 Grain B 28 14 7 0 47 Grain C Nutritionist's requirement 21 25 9 6 38 24 16 8 3.4 (A1). Please help Whole Food solve the problem (e.g., in Excel using Solver) and obtain the results. Report the results to the manager of Whole Food in plain English. (5 marks) (A2). Based on your work for Question (A1), how many constraints regarding the nutrients are binding? For each of the non-binding constraints, what is the surplus? (5 marks) (A3). How sensitive is Whole Food's blending strategy to the cost per pound for each type of grains individually? Which is it most sensitive to? (5 marks) (A4). If the cost of Grain A changes to 37 cents per pound, while all other costs remain the same, should Whole Food keep its current blending strategy or change it? Why or why not? (5 marks) (A5). If the nutrient requirement for Nutrient 2 increases from 16 units to 18 units, should Whole Food keep its current blending strategy? Why or why not? (5 marks) A local caf, the Cool Caf, keeps record of its demand for blueberry muffins to help with the demand forecasting. The following table provides demand figures and forecasts for at six-week period. The demand column shows the actual demand that was experienced for the period. The exponentially smoothed forecast is the calculated forecast for each week using the exponential smoothing method and an alpha factor (a) of 0.25. 1 2 4 5 6 Week Actual Demand 280 248 277 263 269 209 Forecast (exponential smoothing with a= 0.25) 262 267 262 266 265 266 (B1). Calculate the exponentially smoothed forecast of the blueberry muffins demand for Week 7 using an alpha factor (a) of 0.25. (4 marks) (B2). Calculate a three-week simple moving average forecast of the blueberry muffins demand for Week 7. (3 marks) (B3). Calculate a four-week weighted average forecast of the blueberry muffins demand for Week 7 using the weights: 0.4, 0.3, 0.2, and 0.1. (3 marks) (B4). The manager of the Cool Caf found the forecasts are very stable. For example, the forecasts are between 262 and 267, while the actual demand varies from 280 to 209. To make the forecasts more responsive to the changes in actual demand, the manager plans to use a smaller value of alpha factor (say, a-0.15) in forecasting. Would you agree with the manager? Why or why not? (5 marks) (B5). The manager of the Cool Caf wasn't able to explain what made this forecasting "exponential," so he decided to switch to simple moving average forecasting. How many weeks should he include in his forecast, in order to be consistent with his old. exponential smoothing model? (5 marks) (B6). The demand experienced by the caf can show different patterns. Describe one possible cause for seasonal demand patterns, and one possible cause for cyclical demand patterns, that may have influenced the actual demand for the caf. (5 marks) The Whole Food Nutrition Center uses three bulk grains, A, B, and C, to blend a natural cereal that it sells by the pound. The cost of each bulk grain is indicated in the table below, along with the units of four types of nutrient (Nutrient 1, 2, 3, and 4) that is contained in each pound of the grains. After consulting with the nutritionist, Whole Food has determined that each pound serving of the cereal should contain 24 units of Nutrient 1, 16 units of Nutrient 2, 8 units of Nutrient 3, and 3.4 units of Nutrient 4. Whole Food wishes to decide how to blend the three types of grain in order to minimize the total cost of each pound of the cereal. In other words, they wish to solve the following optimization: Minimize 33A + 47B + 38C Subject to: Nutrient 1. Nutrient 2 Nutrient 3 Nutrient 4 22A + 28B + 21C 24 16A + 14B + 25C 16 8A+7B +9C 28 5A A+ B + C =1 A,B,C 20 +66231 Cost per pound of grain (cents) Grain A 22 16 8 5 33 Grain B 28 14 7 0 47 Grain C Nutritionist's requirement 21 25 9 6 38 24 16 8 3.4 (A1). Please help Whole Food solve the problem (e.g., in Excel using Solver) and obtain the results. Report the results to the manager of Whole Food in plain English. (5 marks) (A2). Based on your work for Question (A1), how many constraints regarding the nutrients are binding? For each of the non-binding constraints, what is the surplus? (5 marks) (A3). How sensitive is Whole Food's blending strategy to the cost per pound for each type of grains individually? Which is it most sensitive to? (5 marks) (A4). If the cost of Grain A changes to 37 cents per pound, while all other costs remain the same, should Whole Food keep its current blending strategy or change it? Why or why not? (5 marks) (A5). If the nutrient requirement for Nutrient 2 increases from 16 units to 18 units, should Whole Food keep its current blending strategy? Why or why not? (5 marks) A local caf, the Cool Caf, keeps record of its demand for blueberry muffins to help with the demand forecasting. The following table provides demand figures and forecasts for at six-week period. The demand column shows the actual demand that was experienced for the period. The exponentially smoothed forecast is the calculated forecast for each week using the exponential smoothing method and an alpha factor (a) of 0.25. 1 2 4 5 6 Week Actual Demand 280 248 277 263 269 209 Forecast (exponential smoothing with a= 0.25) 262 267 262 266 265 266 (B1). Calculate the exponentially smoothed forecast of the blueberry muffins demand for Week 7 using an alpha factor (a) of 0.25. (4 marks) (B2). Calculate a three-week simple moving average forecast of the blueberry muffins demand for Week 7. (3 marks) (B3). Calculate a four-week weighted average forecast of the blueberry muffins demand for Week 7 using the weights: 0.4, 0.3, 0.2, and 0.1. (3 marks) (B4). The manager of the Cool Caf found the forecasts are very stable. For example, the forecasts are between 262 and 267, while the actual demand varies from 280 to 209. To make the forecasts more responsive to the changes in actual demand, the manager plans to use a smaller value of alpha factor (say, a-0.15) in forecasting. Would you agree with the manager? Why or why not? (5 marks) (B5). The manager of the Cool Caf wasn't able to explain what made this forecasting "exponential," so he decided to switch to simple moving average forecasting. How many weeks should he include in his forecast, in order to be consistent with his old. exponential smoothing model? (5 marks) (B6). The demand experienced by the caf can show different patterns. Describe one possible cause for seasonal demand patterns, and one possible cause for cyclical demand patterns, that may have influenced the actual demand for the caf. (5 marks)