Question 1 Easter is just around the corner! Hot cross buns are traditionally eaten over the Easter religious Christian holiday to symbolise the crucifixion of Jesus on Good Friday on the cross. A popular local bakery in Reservoir, Jonathan's Bakery, bakes three kinds of hot cross buns: Traditional Hot Cross Buns 6-pack, Extra Soft Fruitless Hot Cross Buns 6-pack and Cadbury Hot Cross Buns made with Cadbury Chocolate 6-pack. Jonathan (the owner of the local bakery) estimates that the bakery can sell 500 6-pack of its Traditional Hot Cross Buns plus 5 extra 6-packs for every dollar it spends on promoting this product; 700 6-packs of the Extra Soft Fruitless Hot Cross Buns plus 6 extra 6-packs for every dollar spent promoting this product; and finally, 900 6-packs of the Cadbury Hot Cross Buns made with Cadbury plus 8 extra 6-packs for every dollar spent promoting this product this year. Although all 6-pack of hot cross buns sell for $4.00, the cost of producing the different hot cross buns varies. It costs Jonathan's Bakery $2.00 to bake a Traditional Hot Cross Buns 6-pack, $1.50 to bake an Extra Soft Fruitless Hot Cross Buns 6-pack and $2.50 to bake a Cadbury Hot Cross Buns made with Cadbury Chocolate 6-pack. Jonathan wants to make sure the bakery bakes the amount of each kind of hot cross buns that the bakery can sell. A budget of $2,000 has been approved for promoting the three kinds of hot cross buns, and at least $500 must be spent advertising each kind of hot cross buns. (i) Formulate a linear programming (LP) model to determine how many 6-packs of the hot cross buns of each kind should be baked, and how do you suggest that Jonathan should allocate the promotional budget if it wants to maximise profits for the bakery? (8 marks) The LP model has been solved, and the sensitivity analysis report has been generated. For the following questions, please refer to the sensitivity analysis report below. A B 1 Microsoft Excel 16.0 Sensitivity Report C D E F G H 2 Worksheet: [Question 1.xlsx] Normal 3 4 Variable Cells 5 6 Cell Name Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 7 $B$10 Number of packs, Traditional Hot Cross Buns 6-pack 3000 0 2 1 1E+30 8 $C$10 Number of packs, Extra Soft Fruitless Hot Cross Buns 6-pack 6700 0 2.5 1E+30 0.5 9 $D$10 Number of packs, Cadbury Hot Cross Buns 6-pack 4900 0 1.5 0.375 1E+30 10 $B$11 Advertising in dollars ($), Traditional Hot Cross Buns 6-pack 500 0 -1 5 1E+30 11 $C$11 Advertising in dollars ($), Extra Soft Fruitless Hot Cross Buns 6-pack 1000 0 -1 1E+30 12 $D$11 Advertising in dollars ($), Cadbury Hot Cross Buns 6-pack 500 0 -1 3 1E+30 13 14 Constraints 15 Final Shadow Constraint Allowable Allowable 16 Cell Name Value Price R.H. Side Increase Decrease 17 $B$17 selling amount of Traditional Hot Cross Buns 6-pack LHS 500 2 500 1E+30 3000 18 $B$18 selling amount of Extra Soft Fruitless Hot Cross Buns 6-pack LHS 700 2.5 700 1E+30 6700 19 $B$19 selling amount of Cadbury Hot Cross Buns 6-pack LHS 900 1.5 900 1E+30 4900 20 $B$20 promotion budget LHS 2000 14 2000 1E+30 500 21 $B$21 promotional requirements for Traditional Hot Cross Buns 6-pack LHS 500 -5 500 500 500 22 $B$22 promotional requirements for Extra Soft Fruitless Hot Cross Buns 6-pack LHS 1000 0 500 500 1E+30 23 $B$23 promotional requirements for Cadbury Hot Cross Buns 6-pack LHS 500 -3 500 500 500 (ii) How many 6-packs of the hot cross buns of each kind should be baked, and how do you suggest that Jonathan should allocate the promotional budget if it wants to maximise profits for the bakery? What is the total profit? (2 marks) (iii) Define Reduced Cost in your own words. Why are all the Reduced Cost equal to 0 in the sensitivity analysis report? (2 marks) (iv) Jonathan received some excellent news from his Cadbury Chocolate supplier. He was informed that the Cadbury Chocolate would be cheaper than initially quoted. Would the optimal solution change if the cost of Cadbury Hot Cross Buns made with Cadbury Chocolate 6-pack decreases by $1 per pack? In addition, what would you expect to happen with the overall profit if the cost of Cadbury Hot Cross Buns made with Cadbury Chocolate 6-pack decreased by $1? Explain your answer. (4 marks) (v) Write down the range of feasibility for the three selling amount constraints. Label your answers clearly. (3 marks) (vi) Jonathan is considering varying the promotional requirement allocation to the Extra Soft Fruitless Hot Cross Buns 6-pack. Would the solution change if the requirement promotional requirements for Extra Soft Fruitless Hot Cross Buns 6-pack were increased to $750 instead of being at $500? Explain your answer. (3 marks) (vii) Jonathan wants to find out the marginal profit change per hot cross bun in the Traditional Hot Cross Buns 6-pack if the demand is 450 packs instead of 500 packs. What is this marginal profit change per hot cross bun in this situation? Explain your answer. END OF SECTION 1 (3 marks)