Question 1 (8 marks) Carly Holdings is one of the companies that supply personal protective equipment (PPE) for healthca

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Question 1 (8 marks)
Carly Holdings is one of the companies that supply personalprotective equipment (PPE) for healthcare workers in Kedah. It hastwo factories in different locations around the state where theyproduce PPE and other safety equipment. They ship the PPEs to threehospitals on a weekly basis. The factories have a weekly productionrates of 400 and 200 PPEs. These PPEs must be shipped to threehospitals that have a demand of 250, 100, and 250 units. The cost(in RM) to ship between each location is known (see the tablebelow). Which factory should produce and ship how many PPEs towhich hospitals to meet the demand at each location with minimalcost?
Cost (RM) Hospital Sultanah Bahiyah Hospital Jitra HospitalSultan Abdul Halim Supply Factory
A 55 30 40 400 Factory
B 35 30 10 200 Demand 250 100 250
(a) What is the objective function for this problem? (2marks)
(b) Find initial basic feasible solution for given problem byusing North-West corner method (6 marks)
Question 2 (8 marks)
An ice cream seller, when deciding how much ice cream to order(a small, medium, or large order), takes into consideration theweather forecast (cold, warm, or hot). There are nine possiblecombinations of order size and weather, and the payoffs (profit)for each are shown in table below.
Order/Weather Cold Warm Hot
Small RM350 RM300 RM250
Medium RM300 RM600 RM400
Large RM200 RM400 RM850
The highest payoffs for each order size occur when the ordersize is most appropriate for the weather, i.e., small order in coldweather, medium order in warm weather, large order/ in hot weather.Otherwise, profits are lost from either unsold ice cream or lostpotential sales. Determine the best decision using the followingcriteria:
(a) Maximax (2 marks)
(b) Maximin (2 marks)
(c) Equal likelihood (2 marks)
(d) Develop an appropriate decision table to determine the bestdecision. (2 marks)
Question 3 (8 marks)
An automated teller machine (ATM) is located near the U-ASSISTin UUM. The machine with a Poisson arrival rate and an exponentialservice time has customers arriving an average of 10 in one hour.Each customer takes approximately 5 minutes to use the ATMservice.
(a) Determine the probability of no customer in the queuingsystem. (2 marks)
(b) Determine the average number of customers in the waitingline. (2 marks)
(c) The bank is intended to add a new ATM at the same location.Determine the changes in the average number of customers in thewaiting line for the current alternative. (4 marks)
Question 4 (8 marks)
A sales manager of OPPO branch wants to determine the weeklyorder size for the OPPO F9. The cost for each handphone is RM 1199while the price is RM 1399 per unit. The demand is probabilistic,and their distributions are given below:
Demand/week Probability 0 0.2 , 1 0.4 ,2 0.3 ,3 0.1
(a) Simulate trials for 4 weeks using random number from thefirst column of table in the Attachment B. (4 marks)
(b) What is the average number of sales per week over the 4weeks period? (2 marks)
(c) What is the average profit per week over the 4 weeks period?(2 marks)
Question 5 (8 marks) An insurance company wants to predict therelationship between driving experiences (in years) and monthlyauto insurance premiums. It is expected that the insurance premiumdepends on the driving experiences. A random sample of five driversinsured with a company and having similar auto insurance policieswas selected.
Driver Driving Experience (years) Monthly Auto Insurance Premium(RM) 1 5 64 2 2 87 3 12 50 4 9 71 5 15 44 (a) Develop a simpleregression equation for this case. (6 marks) (b) If a driver has 7years driving experience, what is the value of monthly autoinsurance premium? (2 marks)