Neilsen Cookie Company sells its assorted butter cookies in containers that have

Question

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 600,000 1-lb containers. The setup cost for each production run is $517, and the manufacturing cost is $0.6 for each container of cookies. The cost of storing each container of cookies over the year is $0.42. 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 5, show that the total production cost is given by the function below. Then minimize the function C on the interval (0, 600,000). (Round your answer to the nearest whole number.)

Explanation / Answer

set up cost = 600000*517 = 310200000

For x production = 310200000/x

Average cost = 0.42x/2 = 0.21x

Manufacturing = 0.6*600000 = 360000

C (x) = 310200000/x + 0.21x + 360000

To minimize x d/dx c(x) = 0

-310200000/x2 + 0.22 = 0

x = 37549.96

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