A restaurant has an annual demand for 882 bottles of California wine. It costs $1 to store 1 bottle for 1 year, and it costs $6 to place a reorder. Find the optimum number of bottles per order.

73 bottles

Explanation:

Let x = total number of orders

C (x) indicates number of orders and the cost of storage

Thus,

6$ dollar to place a reorder

So,

C (x) = 1 (882/x) + 6x = 882/x+6x

C' (x) = -882/x^2+6=0

6=882/x^2.

Thus,

x^2=882/6

Which indicates 882/12=73 bottles of wine per order

Thus C (12) = 1*73+6*12=$145 per year

The best possible number of bottles per order = 73 bottles