Using the DET$2$TL program, recommend the most profitable configuration of a two$-$machine deterministic processing time line. The machines are the same as those in Practice Problem $2.$ Now, there is no target production rate. Instead, we want to maximize the profit rate.

The profit rate is defined as the rate of revenue minus the rate of costs. To simplify this greatly in this case, we will assume that the revenue per part is $$10,000.$ Therefore, the rate of revenue is $$10000P$ per minute, where $P$ is the production rate in parts per minute. The only costs we consider is the inventory holding cost, which is $$10$ per part in the buffer per minute, or $$\frac{10}{b}ar(n).$ Therefore, we must chose the version of the first machine and the buffer size to

maximize $10000P-\frac{10}{b}ar(n)$

Let's access line $M_{11}-M_2$ first. Only use integer $N$ for input.

What is the optimal profit rate? Round to nearest integer

What is the optimal $N?$

Let's access line $M_{12}-M_2$ first. Only use integer $N$ for input.

What is the optimal profit rate? Round to nearest integer

What is the optimal $N?$

What is the production rate of the optimal line? Round to $4$ decimals.