You manage a business specializing in heat-treating industrial castings. Each day, you receive a number of castings for treatment, which follows a Poisson distribution with a mean of 4.1. These castings are processed in a high-temperature oven with a maximum capacity of 5 castings. The oven's heating element may fail with varying probabilities depending on its day of use:

• Day 1: 1% failure probability
• Day 2: 7% failure probability
• Day 3: 9% failure probability
• Day 4: 15% failure probability
• Day 5: 25% failure probability

After the fifth day of use, safety regulations require the heating element to be replaced, regardless of its condition. If the heating element fails on any given day, you must wait until the next day to reprocess the castings from that day. On functional days, the oven can process up to 5 castings, but on failure days, it processes 0 castings.

Castings are processed on a first-come, first-served basis. Any castings that cannot be processed on a given day are stored in a queue and addressed the following day.

You are evaluating 5 different policies, each defined by a parameter d where d can be 1, 2, 3, 4, or 5. According to each policy, if the heating element has been used for d days and has not failed, it will be replaced at the end of the day. If the element fails on any day, it is also replaced at the end of that day.

The financial aspects are as follows:

• Replacing the heating element costs $800 if it has not failed
• If the heating element fails, replacing it costs $1500
• You earn $200 for each casting that is successfully processed
• Each day a casting remains in the queue costs you $40 in lost goodwill and storage costs

Assume all other costs and revenues are negligible. Your goal is to determine through simulation the policy value d (from 1 to 5) that maximizes the expected profit over a 60-day period, assuming you start with a new heating element on the first day. Additionally, you are also interested in whether the queue of unprocessed castings left at the end of the day exceeds 10 at any time during the 60-day period. With the optimal value of d, what is the probability of this event? Please run 5000 simulations.