Let the number of automobiles orders per be represented by p
Let the number of automobiles per orders be represented by y
We shall assume that any time an order is made, some vehicles are sold while others remain in the storage. We shall assume that the orders in the storage spend half the time before a reorder is done.
The reorder interval is days
From the assumption made above, it can be implied that an automobile spends days in the store.
The cost per day of storing an automobile will be
The cost of storing an automobile for days will be
But we have 600 automobiles, hence total storage cost would be
The cost of making a single order is
If p number of orders are made, then the total costs for all orders in a year would be
Hence, the total cost for p orders would be
The total cost, R(y) would be a summation of all the costs. Therefore
Differentiating the above equation with respect to y, we get
The minimum is at a point when
Number of orders to be done are
The minimum total cost is given by
But y= 18
Kaplan, Wilfred. Maxima and Minima with Applications: Practical Optimization and Duality. New York: John Wiley & Sons, Inc., 2011.
Stewart, James. Calculus. 8th. Boston: Cengage Learning, 2016.