Your task in this assignment is to ensure that the manufacturing process at Gainsborough Brewery is both stable and capable and that the total cost of quality is as low as possible. To achieve this, you will face the following challenges:

Challenge $1(20\%)$: You will calculate control limits for X$-$bar and R charts. Simulate daily production, one batch at a time, by clicking $$Run Next Batch$$ repeatedly. With each click, the simulation will generate the next batch processed, draw a random sample from the batch, and calculate the mean and range of the sample. Run your cursor over the points on the X$-$bar and R charts to see the explicit values. Be sure to copy the sample means and ranges to Minitab in order to calculate the control limits for this process. Remember to save your file. You$$ll need to use these control limits in Challenge #$2.$ Note that a production shift $$ an entire day of production $--$ starts at $7$:$00$ a$.$m$.$ and ends at $10$:$00$ p$.$m$.$