Quantitative problems: 1- (20 Points) Review the process diagram below for a car exhaust inspection (egzoz testi) facility with 1 inspector. Answer the questions below. After a car arrives; inspector checks paper work and sets up machine Machines collects exhaust emission data 4 min. per car 8 min. per car 6 min. per car 2 min. per car a) Whichpartoftheprocessisthebottleneckandwhy?(5points) b) What is the cycle time and throughput time? (5 points) c) Whatisthecapacityofthissystem(e.g.perhour)?(5points) d) What impact does adding a second inspector have on the capacity? (5 points) 2- (35 Points) Kristin has decided to start a new business of baking and selling cookies to order and cater to the university students on campus when they study in the evenings and stay up till after midnight. She has named her business Cookie Cult. The following is the list of tasks she came up with for completing one cycle of cookie production. Inspector checks emission data and prepares report Inspector collects payment for the service

Preceding Time Task Tasks (seconds) A - Receive order - 30 B - Clean equipment from previous run C - Program mixer D - Mixer produces the cookie mix E - Prepare baking tray for oven F - Program oven G - Oven bakes cookie H - Cool and box cookies A 40 A 15 B, C 60 D 20 D 15 E, F 50 G 30 I - Accept payment and deliver H 20 cookies On a typical evening (5 PM to 2AM), Cookie Cult expects to receive and fulfil 400 such orders. Kristin wants to set up an assembly-like system to meet this demand. Your job is to help her set up and balance the assembly line in order to facilitate a fast-paced production. Kristens employees may still perform manual work at various stages of the process but assume there are enough skilled employees on hand. a) Drawaprecedencediagramofthetasks.(7points) b) What is the workstation cycle time? (7 points) c) Whatistheoreticalminimumnumberofworkstations?(7point) d) Balance the assembly line using the shortest task time as the primary rule. Show the details of your work. (14 points)

3- (30 Points) A fast-food restaurant has one drive-through window. On average, 40 customers arrive per hour at the window. It takes an average of 1 minute to serve a customer. Assume that interarrival and service times are exponentially distributed. a) Whatistheutilizationoftheserver?Whatfractionofthetimeistheserver idle? (6 points) b) On average how many customers are in the restaurant at any given point in time? (6 points) c) On average how long does a customer spend at the restaurant? (6 points) d) Suppose the restaurant hires one more employee. Recalculate your results for part c) and compare the outcome. Assume that ! is given as 0.076. (6 points) e) Assume the original scenario in the problem statement (not the addition in part d)) and suppose that the restaurant buys new kitchen tools, resulting in the reduction of service time to 0.8 minutes per order. The service time is now assumed constant. Recalculate and compare your results in parts c and d). Which scenario is better in terms of average time spent in the restaurant; with two employees or with the new kitchen tool?