Carly Holdings is one of the companies that supply personal protective equipment (PPE) for healthcare workers in Kedah. It has two factories in different locations around the state where they produce PPE and other safety equipment. They ship the PPEs to three hospitals on a weekly basis. The factories have a weekly production rates of 400 and 200 PPEs. These PPEs must be shipped to three hospitals that have a demand of 250, 100, and 250 units. The cost (in RM) to ship between each location is known (see the table below). Which factory should produce and ship how many PPEs to which hospitals to meet the demand at each location with minimal cost?
Cost (RM) Hospital Sultanah Bahiyah Hospital Jitra Hospital Sultan 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?
(b) Find initial basic feasible solution for given problem by using North-West corner method
Question 2
An ice cream seller, when deciding how much ice cream to order (a small, medium, or large order), takes into consideration the weather forecast (cold, warm, or hot). There are nine possible combinations 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 order size is most appropriate for the weather, i.e., small order in cold weather, medium order in warm weather, large order/ in hot weather. Otherwise, profits are lost from either unsold ice cream or lost potential sales. Determine the best decision using the following criteria:
(a) Maximax
(b) Maximin
(c) Equal likelihood
(d) Develop an appropriate decision table to determine the best decision.
Question 3
An automated teller machine (ATM) is located near the U-ASSIST in UUM. The machine with a Poisson arrival rate and an exponential service time has customers arriving an average of 10 in one hour. Each customer takes approximately 5 minutes to use the ATM service.
(a) Determine the probability of no customer in the queuing system.
(b) Determine the average number of customers in the waiting line.
(c) The bank is intended to add a new ATM at the same location. Determine the changes in the average number of customers in the waiting line for the current alternative.
Question 4
A sales manager of OPPO branch wants to determine the weekly order size for the OPPO F9. The cost for each handphone is RM 1199 while 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 the first column of table in the Attachment B.
(b) What is the average number of sales per week over the 4 weeks period?
(c) What is the average profit per week over the 4 weeks period?
Question 5 An insurance company wants to predict the relationship between driving experiences (in years) and monthly auto insurance premiums. It is expected that the insurance premium depends on the driving experiences. A random sample of five drivers insured with a company and having similar auto insurance policies was 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 simple regression equation for this case. (b) If a driver has 7 years driving experience, what is the value of monthly auto insurance premium?
