P66794A 4 3. Donald plans to bake and sell cakes. The three types of cake that he can bake are brownies, flapjacks and muffins. Donald decides to bake 48 brownies and muffins in total. Donald decides to bake at least 5 brownies for every 3 flapjacks. At most 40% of the cakes will be muffins. Donald has enough ingredients to bake 60 brownies or 45 flapjacks or 35 muffins. Donald plans to sell each brownie for £1.50, each flapjack for £1 and each muffin for £1.25 He wants to maximise the total income from selling the cakes. Let x represent the number of brownies, let y represent the number of flapjacks and let z represent the number of muffins that Donald will bake. Formulate this as a linear programming problem in x and y only, stating the objective function and listing the constraints as simplified inequalities with integer coefficients. You should not attempt to solve the problem. (Total for Question 3 is 9 marks) P66794A 5 4. B 2 25 25 E 5 56 56 A 1 0 0 C 3 35 37 35 F 6 63 63 D 4 42 45 42 G 7 66 74 70 68 66 Figure 2 Dijkstra’s algorithm has been applied to the network in Figure 2. A working value has only been replaced at a node if the new working value is smaller. (a) State the length of the shortest path from A to G. (1) (b) Complete the table in the answer book giving the weight of each arc listed. (Note that arc CE and arc EF are not in the table.) (3) (c) State the shortest path from A to G. (1) It is now given that •  when Prim’s algorithm, starting from A, is applied to the network, the order in which the arcs are added to the tree is AB, BC, CD, CE, EF and FG •  the weight of the corresponding minimum spanning tree is 80 •  the shortest path from A to F via E has weight 67 (d) Determine the weight of arc CE and the weight of arc EF, making your reasoning clear. (3) (Total for Question 4 is 8 marks) TOTAL FOR DECISION MATHEMATICS 1 IS 40 MARKS END P66794A 6 BLANK PAGE P66794A 7 BLANK PAGE P66794A 8 BLANK PAGE Turn over Pearson Edexcel Level 3 GCE Candidate surname Other names Total Marks Centre Number Candidate Number Please check the examination details below before entering your candidate information Paper reference P66794A ©2021 Pearson Education Ltd. 1/1/1/1/1/ Answer Book Do not return the question paper with the answer book. Further Mathematics Advanced Subsidiary Further Mathematics options 27: Decision Mathematics 1 (Part of options D, F, H and K) 8FM0/27 2 1. _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________