1. [15 points] How may units need to be started through a manufacturing process that has a process yield of 0.97 in order to get 1,397 non-defective units from the process? Consolidated Corp. is a manufacturer that produces metal parts. Recently, it signed a contract to supply metal plates to an air conditioning manufacturer. The specications require the length to be between 14.95 cm and 15.05 cm. With the current production process, Consolidated Corp. manages to produce plates whose length is, on average, equal to 15 cm; however, a closer inspection reveals some variability in the process, with the length of the plate being normally distributed with standard deviation equal to 0.015 cm. a. [15 points] What is the capability index (score) of Consolidated Corp? b. [15 points] What is the minimum standard deviation allowed for the process to meet the rigorous six-sigma standards? [15 points] Consider the following two production processes making an electronic component for a navigation system. Both processes consist of 25 steps and operate at a cycle time of 0.75 min/unit. Their most error prone operation is step 12. Process 1: Has a nal inspection at the end of the process and has 128 units of inventory between step 12 and the inspection. Process 11: has each worker check the work of the previous steps and has 240 units of inventory between step 12 and the end of the process, roughly equally distributed across the remainder of the process. What would be the information turnaround time for a defect made at step 12? 4. A toy company currently operates for 40 hours per week and sells and average of 6,000 toys per week. The manufacturing process consist of three basic operations: molding, painting and nishing (performed in that order). Changing over between different versions of toys requires setup time at the painting and nishing. The table below lists the setup times for a batch and the processing times for each unit at each step. There is unlimited buffer space between these steps. Assume that (i) setups need to be completed rst, (ii) a setup can only start once the batch has arrived at the resource, and (iii) all ow units of a batch need to be processed at the resource before any of the units of the batch can be moved to the next resource. PROCESS STEP MOLDING PAINTING FINISHING SETUP TIME No setup 20 mins 10 mins PROCESSING TIME 0.3 mins/unit 0.2 mins/unit 0.15 mins/unit a. [10 points] What is the process capacity in units per hour with a batch size of 600 toys? b. [15 points] What batch size would minimize inventory without decreasing the process capacity? c. [15 points] What batch size would minimize inventory without decreasing the current ow rate