PARTA FOUR QUESTIONS ANSWER THREE Question 1 1A) (a) Using practical examples from the field of business compare and con
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- Parta Four Questions Answer Three Question 1 1a A Using Practical Examples From The Field Of Business Compare And Con 1 (60.85 KiB) Viewed 83 times
(a) Formulate a linear programming (LP) model. Major Topic:2 Blooms Designation EV Score Transportation problem 7 The model in (A) was solved using Solver and part of the Solver output is shown below. Use it to answer the questions that follow. Adjustable Cells Cell Name Original Final Value Value 80 80 0 0 0 0 0 SCS4 Koforidun Sunyani SD$4 Koforidua Cape Coast SES4 Koforidua Ho SCS5 Accra Sunyani SDS5 Accra Cape Coast SESS Accra Ho SCS6 Kumasi Sunyani SDS6 Kumasi Cape Coast SES6 Kumasi Ho 10 60 0 100 0 10 60 0 100 0 0 (b) As a management science student the MD of the company seeks your expert advice on ways in which to determine the optimal transportation rule. Advise the MD, providing detailed explanation using the table above. Write your answer in a form of a report to the MD. Seore Major Topic:2 Transportation problem Blooms Designation AP 6 TOTAL SCORE:20 Question 2 2A) Using practical example from the field of business, compare and contrast the relationship between linear programming and assignment problems. Illustrate your understanding of these concepts by discussing and explaining possible four reasons for the differences using a practical examples business Major Topic: 1 Blooms Designation Score Linear programming and 7 Assignment problems AP 7 2B) ) Wilmar Company Ghana has to optimize a production plan for four (4) products, Lux, Frytol, Lipton, and Close-up. Each product is completed through three (3) production operations -Machining, Assembly, and packaging available man-hours. There are 400 for machining, 480
10 Lux order Usage 100 -5.22 100 284.61538 100 The computer solution of the production-planning problem for the four (4) products is as follows and includes the optimal values of decision variables and sensitivity output 6 b) Management have asked you to determine the optimal solution. Write your answer in a form of a report to be submitted to the management. Score 6 Major Topic:1 : Blooms Designation Linear programming AP TOTAL SCORE:25 : Question 3 The weekly demand for a product, which is held in stock is always 90 units. When an order for new stock is placed, it is delivered almost instantaneously by an ordering cost of 50,000 is incurred. The product costs 3,000 per unit, and it costs 15 percent of this amount to hold a unit in stock for a year. Currently, orders are placed for 2000 units. There are 50 working weeks in a year and lead time is one week. a) As a management science student, the MD of the company seeks your expert advice on ways in which to determine the economic order quantity, optimal order cycle time, re-order level and total annual inventory cost. Advise the MD, providing detailed explanation using your answer. Write your answer in a form of a report to the MD. b) Advise the MD about savings, if any, could be made by changing from current order quantity of GHe 2000 units to the one obtained in (a) above. . Major Topic: 8 Blooms Designation Score Inventory management 7 c) Describe the order policy followed by the firm based on your calculations. Major Topic: 8 Blooms Designation Score AN AP 7 7 Inventory 6 TOTAL SCORE:20 Question 4 (A) () A and C mall is a busy centre for residents in East Legon and its sourrounding community. Assume that 2 customers arrive every 12
2B) Wilmar Company Ghana has to optimize a production plan for four (4) products, Lux, Frytol, Lipton, and Close-up. Each product is completed through three (3) production operations - Machining, Assembly, and packaging available man-hours. There are 400 for machining, 480 hours for assembly 220 hours for packaging. Data for the production plan. Production Time (Hour/unit) Available Lux Frytol Lipton Close-up Machining 0.7 0.75 0.55 0.34 Assembly 0.82 0.55 Packaging 0.24 0.32 0.45 0.27 Raw Frytol Lipton Close-up material 1.9 2.5 1.8 2 unit 0.55 0.8 400 480 220 Lux 4.80 12 6 7.8 Profit per unit (GHC) There are 1500 units of raw materials available, The company has always accepted an order of 100 units of Lux. a) Formulate a linear programming model for this problem Major Topic:1 Linear programming Blooms Designation CR Score 7 5 Adjustable Cells Allowabl Final Reduced Objectiv Allowabl e e Coeffici ent Increase Name Value Cost Decrease Lux 100 0 4.8 TE 30 IE+30 Cell SBS 13 SBS 14 SBS 15 SBS 16 Frytol 330.153 0 12 5.2058 2.25 Lipton 0 - 2.70 6 2.7092 1E+30 Close-up 242 307 0 7.8 1.8 2.36 e Constraints Constrai Allowabl Allowabl Final Shadow nt e R.H. Cell Name Value Price Side Increase Decrease SGS 6 Machining Usage 400 6.923 400 51520754 107.3 SGS 7 Assembly Usage 458.99538 0 0 480 IE+30 21.004615 SGS 8 Packaging Usage 195.07230 0 220 1E IE+30 24.927692 SGS Raw Material 9 Usage 1500 2.72 1500 102.11667 210 SGS 10 Lux order Usage 100 -5.22 100 284.61538 100 The computer solution of the production planning problem for the four (4) nroducts is as follows and includes the antimal values of decision
TWO QUESTIONS ANSWER ALL Question 5 A. The Managing Director of Koala Supermarket is faced with the problem of assigning five senior managers to six regions. From past experience, he knows that the efficiency of the sales and operating cost, depends on manager-region combination. The sales in Ghe) recorded under the different managers are given below Manager Region 4 1 2 2 3 5 6 А 73 91 87 82 78 80 B 81 85 69 76 74 85 72 83 84 78 91 с c D D 75 93 96 86 91 83 82 E 93 91 79 89 69 76 a) Formulate a linear programming model for solving the problem. Major Topic: 3 Score Blooms Designation CR Assignment problem 7 The model above was solved using Solver software and part of the output is shown below. Use it to answer the questions that follow. Original Value Final Value 0 0 0 0 1 1 1 0 0 0 0 0 O 0 0 1 1 Cell Name SCS4 A region SDS4 A region 2 SES4 A region 3 SFS4 A region 4 SGS4 A region 5 SHS4 A region 6 SCSS B region 1 SDSS B region 2 SESS B region SFSS B region 4 SGS5 B regions SHSS B region 6 SCS6 C region ! SDS6 C region 2 SE$6 C region 3 SFS6 C region 4 SGS6 C region 5 0 0 0 0 0 0 0 0 O 0 0 0 0 0 0 0 0 0 10 1 1 0 0 0 0 0 0 SHS6 C region 6 SCS7 D region 1 SDS7 D region 2 SEST D region 3 SFS7 D region 4 SGS7 D region 5 SHS7 D region 6 SCS8 E region 1 SDS8 E region 2 SES E region 3 SFS8 E region 4 SGS E regions SHSS E region 6 1 0 0 1 1 1 0 0 1 0 0 0 O 0 0 0 0
TOTAL SCORE:20 : Question 4 A) (A) A and C mall is a busy centre for residents in East Legon and its sourrounding community. Assume that 2 customers arrive every 12 minutes and 3 customers are served every 15 minutes and that currently, there is only one cashier. a) Determine the average waiting time in minutes before service begins. Major Topic: 7 Blooms Designation Score EV Queuing analysis 3 3 a b) Advice the management the proportion of the time that a customer has to wait. . Major Tople: 7 Blooms Designation Score Queuing analysis EV (B). Management perceives that the waiting time computed in (ii) above is not acceptable and is faced with two options. Management can either employ an assistant for the cashier or open a second cash machine, The former, if implemented, will enable 4 requests to be served every 15 minutes and the assistant will receive a monthly salary of GHC160. The latter, if implemented will improve the arrival rate to customer every 12 minutes. However, it requires an initial capital outlay of GHC3000 and the cashier who will operate the cash machine will receive a monthly salary of GHC250. The shop avoids a loss in sales of GHC80 per month for each minutes that average customer waiting time is reduced. c) Calculate the financial gain to A and C mall under option 1 and advice management on the option. Major Topic: 7 Blooms Designation Score CR Queuing analysis 7 7 c) Calculate the financial gain to A and C mall under option 2, assuming the initial capital outlay is sunk cost and advice management on this option. Major Topic: 7 Blooms Desiguation Score EV Queuing analysis 7 TOTAL SCORE:20 PART B TWO QUESTIONS ANSWER ALL Question 5 A. The Managing Director of Koala Supermarket is faced with the problem of assigning five senior managers to six regions. From past experience, he knows that the efficiency of the same ager-region
SFS8 E region 4 SGS8 E region 5 SHSS E region 6 0 0 0 0 0 0 0 b) Management have asked you to determine the optimal assignment rule. Write your answer in a form of Memo to be submitted to the management Major Topic: 3 Blooms Designation Score AP Assignment Problem 7 c) As a management science student, advice the MD concerning the objective function value, giving a detailed explanation regarding the optimal assignment rule. Major Topic: 3 Score Blooms Designation AN Assignment problem 6 TOTAL SCORE:20 Question 3 A software Company has just won a contract worth GH¢80m, if it delivers a successful product on time, but only GH¢40m, if this is late. It 11 faces a problem of whether to produce the work in-house or to subcontract. To subcontract the work would cost GH¢20m but based on past experience would have only a 90% chance of being successful. In the event of the software not being successful, there would be insufficient time to re-write the whole package internally but there would still be the options of either a late-rejection of the contract (at a further cost of GH¢10m) or a late subcontracting of the work on the same terms as before. With this late start the local subcontractor is estimated to have only a 50/50 chance of producing it late. In this case, the subcontractor still has to be paid GH¢50m, regardless of whether he meets the deadline or not. a) Draw decision tree for the software company Blooms Designation Score Major Tople: 6 Decision analysis CR 7 b) Advice the company with regard to the expected value. Majer Tople: 6 Blooms Designation Score AP Decision analysis 7 Score c) Base on your expert knowledge, advice the company with regard to appropriate expected value. Majer Tople: 6 Blooms Designation Decision analysis TOTAL SCORE:20 AP 12