Johnny's workshop works in lastmile deliveries. It projects to deliver packages around 5 am. If a delivery is late by 1 hour, the company refunds customers 10 dollar worth of rebate. A Taguchi loss function in the form of k(y m)^2 is used in order to discourage the company from missing the target time. If y, the actual delivery time is smaller than the target m, the company is overzealous and, even though this makes customers happy, it adds an unnecessary burden/cost for the company. If y is larger than m, the delivery is late and the function measures a penalty for the client's displeasure.

The company estimates the cost of its delivery process as a linear function as follows: Developing the delivery process to meet the 5 am time mark results in a cost of $25 per delivery. But this cost decreases linearly and can be stated as 25 6(y-m), where m is the target time and y m measures the deviation from the target time.

The two functions put together yield a total cost of TC = k((y m)^2) + 25 6(y-m)

1. Determine the value of k, whereby you measure the deviation in (y m) in hours. 2. What cost does the company incur per delivery if it sticks to its target (5 am), i.e. it is neither ahead nor late. 3. What is the cost in the function TC above if the company delivered packages at 4 am, i.e. one hour ahead of its original target. 4. What is an ideal deviation from the original target (5 am) that the company should consider. 5. What is the total cost, if the company performed with this ideal deviation that you computed above.