A Hotbakery Is A Chained Brand In Hong Kong And Its Well Known Products European Sour Bread Hong Kong Burn And Cup C 1 (260.71 KiB) Viewed 42 times
a HotBakery is a chained brand in Hong Kong, and its well-known products: European Sour Bread, Hong Kong Burn, and Cup Cake has gained wide popularity in the market. The manager realized the needs to develop new products, without interfering the most well-known products. For the first time, the manager consults a management science team and makes use of linear programming formulation to maximize the total profit, meanwhile facilitate his decision making under certain variability and dynamic interaction. The generated sensitivity analysis report is shown as below, where the objective coefficients of the decisions variables Production European Sour Bread, Production Hong Kong Burn, and Production Cup Cake refers to the unit profit (HKD). 4 Answer the following questions using the generated sensitivity report. Note: Each part is independent (i.e. any change made in one part does not apply to any other parts)." Variable Cells Cell Name $C$18 Production European Sour Bread $D$18 Production Hong Kong Burn $E$18 Production Cup Cake Final Reduced Objective Allowable Value Cost Coefficient Increase 336 0 3.1 2.8375 200 4.75 1E+30 260 5 1 E+30 Allowable Decrease 3.1 2.27 3.76 이이 Constraints o Cell Name $F$11 Minimum European Bread Production Used $F$12 Maximum Hong Kong Burn Production Used $F$13 Minimum Hong Kong Burn Production Used $F$14 Minimum Cup Cake Production Used $F$15 Molding (minutes) Used $F$8 Flour (pounds) Used $F$9 Cheese (ounces) Used $F$10 Sugar (pounds) Used Final Value 336 200 200 260 3000 200.4 130 27.12 Shadow Constraint Allowable Allowable Price R.H. Side Increase Decrease 200 1E+30 2.27 200 170 21.66666667 150 50 1E+30 100 160 1E+30 0.62 3000 32.5 680 0 203 1E+30 2.6 7.52 130 170 21.66666667 50 1E+30 22.88 olol lo
a) What is the optimal production quantity? What is the objective function? (4 marks) b) Assume the cost of the ingredient making Hong Kong Burn get increased, resulting the unit profit decreases. Would the optimal production quantity change if the unit profit of Hong Kong Burn is decreased to 4.25? What would be the change in total profit? (4 marks) c) The allowable increase for Minimum European Sour Bread Production Used constraint is missing from the sensitivity report. What numbers should be there? Explain how you were able to deduce the number. (4 marks) d) Suppose the manager wants to develop new products, and revises one of the requirements to "the maximum production quantity of Hong Kong Burn should be 180” instead of 200 that is currently set. What is the change to the total profit? (4 marks) e) Suppose the manager will consider possible man power allocation for the new product of a cheese cake. Before, there were 3000 minutes spent on Molding (minutes), and now it is
decreased from to 2500 to relieve extra manpower. Meanwhile, the Cheese (ounces) Used is increased from 130 to 200 for the ingredients of new products. What can be said about the change of profit? (4 marks)
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