Question: INVENTORY CONTROL AND PLANNING Neilsen Cookie Company sells its assorted butter cookies in containers that have a net content of 1 lb. The estimated demand for the cookies is 1,000,000 1-lb containers. The setup cost for each production run is $500, and the manufacturing cost is $.50 for each container of cookies. The cost of storing each container of cookies over the year is $.40. Assuming uniformity of demand throughout the year and instantaneous production, how many containers of cookies should Neilsen produce per production run in order to minimize the production cost? Hint: Following the method of Example, show that the total production cost is given by the function
C(x) = (500,000,000/x) + (0.2x) + (500,000)
Then minimize the function C on the interval (0, 1,000,000).
Example: Find the relative maxima and relative minima of the function f (x) = x2.