Problem $2.$ An electrical engine company has a production capacity of $120$ engines per month, and sales are observed to be

$100$ engines per month without randomness. An engine costs the company $$75$ to manufacture, while the setup cost of a

production run is $$950.$ Holding costs are figured at $28\%$ per year.

Answer the following questions:

$2\mathrm{.}1)(5$ points$)$ Write down the model name and list all the parameters of the problem and their numerical values $($convert

to yearly rates as necessary$).$

$2\mathrm{.}2)(5$ points$)$ Write down the formula for the optimal number of engines to produce in a production run, and compute it

numerically.

$2\mathrm{.}3)(5$ points$)$ Write down the formulas for the time between production runs $($cycle length$)$ and its uptime and downtime

components, and compute each of them numerically.

$2\mathrm{.}4)(5$ points$)$ When the inventory is at its maximal level in a cycle, what is the amount of dollars tied up in inventory at

that point $($include all formulas$)?$