4. Send Bad company works in last-mile deliveries. It aims at delivering packages around 5 pm. If a shipment is late by 1 hour, the company compensates customers in the form of $10 rebate. A Taguchi loss function in the form of k(y m)² is used in order to deter the company from missing the target time. If y, the actual delivery time, is smaller than the target m, the company is overzealous and, although 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 customer dissatisfaction.

On the other hand, the company estimates the cost of its delivery process as a linear function as follows:

Designing the delivery process to meet the 5 pm time target 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 pm), i.e. it is neither ahead nor late.

3. What is the total cost in the function TC above if the company delivered packages at 4 pm, i.e. one hour ahead of its original target.

4. What is an ideal deviation from the original target (5 pm) that the company should consider.

5. What is the total cost, if the company performed with this ideal deviation that you computed in Question 4.