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加拿大MATH数学代写 Quantitative Modelling代写

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加拿大MATH数学代写

Quantitative Modelling MATH2013

Trimester 2A, 2021

加拿大MATH数学代写 The Main Roads Department is widening the area around two major roads to cater for increased traffic to a new hospital and activity center.

Trimester 2A, 2021 Quantitative Modelling MATH2013

Individual Assignment (25%)

Due Date: Friday, September 10, 2021, by 11:59 PM through Turnitin.

 

Instructions:         加拿大MATH数学代写

  • You will download the assignment, which is a PDF file, and you need to begin to type only your answers in a Word document, excluding thequestions.
  • The assignment must be typed as much as possible.
  • Label all tables and figures correctly.
  • Interpretation must follow the relevant information. All results must be verified by complete workings. Single answers are generally not acceptable in any quantitativeunit.
  • The assignment must include a cover sheet with the student’s full details.
  • The lecturer may request an Excel copy to check on formulas used, so be prepared for this and keep a backup copy.
  • All questions must be attempted.

Question 1 (5 Marks):

A company is considering manufacturing three types of electronic toys: A, B, and C. The projected profit contribution is $5.15, $7.00, and $10.00, respectively. The toys are manufactured in three stages: made, assembled, and painted. The production times in minutes are given below. 加拿大MATH数学代写

  Parts Assembly Paint
A (x1) 8 12 5
B (x2) 11 14 6
C (x3) 18 16 8

The capacity of the parts department is 500 hours per week.

The capacity of the assembly department is 800 hours per week.

The capacity of the paint department is 400 hours per week.

It is necessary to make at least 500 A’s and 1,000 B’s.

a)Manuallyshow the decision variables, objective function, and constraints (at this point, you are setting out the problem. You are not solving the problem).(1 mark) 加拿大MATH数学代写

b)UseExcel to find the best weekly production plan (i.e., you will now solve the problem). State how many of each type of toy must be made and the value of the objective function. If management later decides it is necessary to produce 100 units of C, determine the reduction in profit.(4 marks)

                                                                       Total (5 marks)

Question 2( 4 marks) 加拿大MATH数学代写

An individual wishes to invest $25000 in two types: Investment A yields 15%, and investment B yields 18%. Market research suggests an allocation of at least 35% in A and at most 45% in B. In addition, investment in A should be at least twice the investment in B.

a)Show thedecision variables (0.5 marks)

b)Show theobjective function (0.5 marks)

c)Show and name the constraints in standard form (suitable forusing Excel) ( 1 mark)

d)Solve the problem by using Excel. Do so and write a conclusion of your findings for the person.(2 marks)

                                                                         Total (4 marks)

Question 3 (5 marks):

ABC company has five (5) factories. They send their products through five (5) distribution centers (DCs) that serve a specific market. To use full truckloads and to have the economy of scale in transportation, they also use two cross-dock centers as transshipment points. All the required data are represented in the following tables.

Transportation cost($) Crossdock  加拿大MATH数学代写

Factory Crossdock 1 Crossdock 2
Factory 1 加拿大MATH数学代写 15 40
Factory 2 19 52
Factory 3 29 16
Factory 4 60 15
Factory 5 50 63
Transportation cost($) Distribution Center
Crossdock DC1 DC2 DC3 DC4 DC5
Crossdock 1 10 20 14 35 36
Crossdock 2 40 10 13 17 70

Capacity of Factory (units)

Factory 1 150
Factory 2 加拿大MATH数学代写 320
Factory 3 80
Factory 4 170
Factory 5 200

Demand for each DC (units)  加拿大MATH数学代写

DC 1 140
DC 2 130
DC 3 180
DC 4 250
DC 5 150

 ABC wants to minimize the whole distribution costs. So, please answer the following questions:

a)Developan optimization model to solve the above transshipment  Please clearly define the decision variables, constraints that must be satisfied, and objective function with the corresponding explanations.( 2 marks) 加拿大MATH数学代写

b)How many units of products are transshipped to DCs through cross-docks 1 and2?( 1 mark)

c)Which DC’s will be served by each cross-dockcenter?( 1 mark)

d)What is the minimum total distributioncost?(1 mark)

                                                                      Total (5 marks)

加拿大MATH数学代写
加拿大MATH数学代写

Question 4(2 marks):  加拿大MATH数学代写

The table below represents the travel time in minutes between 10 locations in Singapore. Draw the corresponding network and use the shortest route algorithm to find the shortest distance from node 1 to each node and the final location at node 10. Please note that all the branches are two ways which mean they are undirected.

  Start node End node Travel time( minutes)
Branch 1 1 2 15
Branch 2 1 3 14
Branch 3 1 4 12
Branch 4 1 5 17
Branch 5 2 3 7
Branch 6 2 7 19
Branch 7 3 6 8
Branch 8 3 4 11
Branch 9 4 5 13 加拿大MATH数学代写
Branch 10 4 6 8
Branch 11 5 9 11
Branch 12 6 7 12
Branch 13 6 8 6
Branch 14 6 9 15
Branch 15 7 8 9
Branch 16 7 10 15
Branch 17 8 9 12
Branch 18 8 10 17
Branch 19 9 10 15

                                                                                    Total (2 marks)

 

Question 5 (2 marks):

The following table shows a network identified by its starting and ending nodes. The distances between nodes are in miles. Draw the network and use the minimal spanning tree to find the minimum distance required to connect them. Highlight (make bold) the final connections.

Branch name Start node End node  

Distance(miles)

Branch 1 1 2 4
Branch 2 1 3 5
Branch 3 1 4 3
Branch 4 1 5 6
Branch 5 2 3 5
Branch 6 2 8 6
Branch 7 3 6 6加拿大MATH数学代写
Branch 8 3 4 3
Branch 9 3 7 5
Branch 10 4 5 4
Branch 11 4 6 7
Branch 12 5 6 5
Branch 13 5 10 3
Branch 14 6 7 4
Branch 15 6 10 8
Branch 16 7 8 加拿大MATH数学代写
Branch 17 7 10 5
Branch 18 7 11 9
Branch 19 8 9 2
Branch 20 9 11 5
Newrow 21 10 11 7

                                                                                Total (2 marks)

 

Question 6 (2 marks):

In the following table, the branches represent the units of electrical power that can be delivered along with the various links between relay stations in 7 different locations. The numbers in the fourth column in the table represent the maximum associated flow capacities for each branch. By using the maximal flow algorithm, fill in the second table below by showing the routes, the flow along each route, and the total flow. Also, show the blocked routes and flows at the source and sink and the totals.  加拿大MATH数学代写

Branch name Start node End node Capacity
Branch 1 1 2 6
Branch 2 1 3 4
Branch 3 1 4 5
Branch 4 2加拿大MATH数学代写 3 4
Branch 5 2 6 7
Branch 6 3 4 5
Branch 7 3 5 3
Branch 8 3 6 3
Branch 9 4 5 3
Branch 10 4 7 6
Branch 11 5 7 4
Branch 12 6 7 5

                                                                         Total (2 marks)

Question 7 (5 marks)加拿大MATH数学代写

The Main Roads Department is widening the area around two major roads to cater for increased traffic to a new hospital and activity center. This involves laying gas and water pipes and various other activities. For simplicity, these activities have not been named but are labeled A through L. Their immediate predecessors and time requirements are given in the following table.

Activity Optimistic time(a) Most Likely time(m) Pessimistic time(b) Predecessors
A 2 3 4  
B 3 6 9 A
C 2 5 7 B
D 6 12 27 A, B
E 4 6 13 A, B, C
F 11 17 29 D, E
G 6 12 加拿大MATH数学代写 16 E, F
H 3 6 10 A, B, D, E
I 2 5 7 C, D, E, F
J 4 7 13 D, E, F, G
K 3 6 12 D, I, J
L 4 7 15 I, J, K

a)Include columns for expected time (in months) and variance to the above table (include formulas in the table heading). Use two decimal places for expected time and variance.(1 mark)

b)Draw a CPM/Pert diagram of the activities using the followingconvention:

(1 mark)

a)Calculate the expected project length, the variance of the critical path, the standard deviation of the critical path, and the activities along the critical path.(2 marks)

b)What is the probability the project will be completed within the due time of 80months?(1 mark)

                                    Total (5 marks)

加拿大MATH数学代写
加拿大MATH数学代写

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