Reference questions and data provide for each below.

1. A fast food restaurant has customers arrive at the checkout counter at a rate of 35 customers per hour. The average check out time at the till is 85 seconds. 20 marks a) What is the utilization? b) What is probability that there are zero customers at the counter (either in line or being served)? c) What is the probability that there are two or more customers at the checkout counter? d) What is the probability that there are 1 or 2 customers at the counter? e) What is the average number of customers waiting in line? f) If the store wanted the average time in the system to be 5 minutes, what would the service rate have to be? g) What is the probability that checkout time will take between 1 and 2 minutes? h) What is the probability that checkout time will take more than 2 minutes?

2. An operation manager of a chemical manufacturing plant must determine the lot size for a chemical that has a steady demand of 2,550 litres per day. The production rate is 7,350 litres per day, setup cost is $700, annual holding cost is $0.22 per litre, and the plant operates 330 days per year. 20 marks a. Determine the production order quantity (POQ), the number of orders and the time between orders. What is the total annual setup cost? What is the total holding cost per year? Using an appropriately labelled diagram, graph setup cost, holding cost, and total inventory cost, and show the optimal production order quantity and the minimum total inventory cost. What is the setup time in hours, based on a $25 per hour setup labour cost? b. Determine the duration of the active production interval, t. Determine the maximum inventory. Determine demand during the production interval. c. As part of its new JIT program, the company has signed a long-term contract with its customers and the company will take orders electronically for the chemical. The optimal lot size (production order quantity) will drop to 40,000 litres. Determine the new setup cost per order and the number of orders (setups). What is the total annual cost of managing the inventory with the new policy? What is the setup time in hours, based on a $25 per hour setup labour cost with the new policy?

3. You are asked to determine a location for a recycling depot serving three urban centres. They are: 20 marks 1. Smallville, population 1,100, at grid location (1.8, 2.8); 2. Bigburg, population 1,900, at grid location (3.5, 8.1); and 3. Middleton, population 1,350, at grid location (7.8, 6.2). a) Determine the centre of gravity of the three locations. b) It is determined that planners would prefer to have the depot in either Bigburg or Middleton (although it will serve all three centres). Using metropolitan distances, determine the load- distance scores for both Bigburg and Middleton and make a recommendation as to which town should have the depot. c) You are asked to provide input on a layout for a new office. The old layout is thought of as being inefficient. You are asked to redesign the layout and evaluate your redesign using load distance scores. The current layout is shown below. The overall shape cannot change; you can merely move the individual departments around. (8 marks) E D C B A Trips between the different departments are as follows: AB : 8 trips per day, AC : 4, AD : 7, AE : 12 BA : 5, BC : 2, BD :5 , BE : 3 CA : 3, CB : 5, CD : 12, CE : 3 DA : 14, DB : 10, DC : 4, DE : 9 EA : 2, EB : 3, EC : 5, ED : 3