Exercise $1$: Economic Order Quantity. $(35$ points$)$

One of the Toyota plants must decide how many of a particular type to order for manufacturing automobiles.

The company plans to produce $300,000$ cars in the next year. All cars planned for production use the same headlights $(2$ units per car$)$; therefore, demand for the headlights for the next year is known to be $600,000$ units. The purchasing agent wants to know how many headlights to buy at one time. Historically, headlights have been received half a day $($lead time$)$ after they were ordered. It costs $50$ to order lights, and the holding$-$cost fraction used by the auto company is $22\%$ per year. The headlights cost $25$ each.

Compute the Economic Order Quantity.

What is the number of orders per year?

What is the frequency of orders? Assume the company works $365$ days a year.

What is the reorder point?

The company works with a Safety Stock of $0\mathrm{.}75$ days. What is the level of this stock?

What is the Average Stock?

What is the total Holding Cost?

What is the total Ordering Cost?

What is the total Cost of Stock Management?

Draw the evolution of stock in time $($the stock chart$).$