SOLUTION: Please help me to solve this problem. In his model for storage and shipping costs of materials for a manufacturing process, Lancaster derives the cost function : {{{C(k)=100(100+9k

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Question 464081: Please help me to solve this problem. In his model for storage and shipping costs of materials for a manufacturing process, Lancaster derives the cost function : C%28k%29=100%28100%2B9k%2B144%2Fk%29, 1 ≤ k ≤ 100 , where C(k) is the total cost (in dollars) of storage and transportation for 100 days of operation if a load of k tons of material is moved every k days. Find C(1). For what value of k does C(k) have a minimum ? what is the minimum value ?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
C(1) = 100(100 + 9 + 144) = 25,300 $ total cost of storage and transportation.
C%28k%29=100%28100%2B9k%2B144%2Fk%29 ==> dC%28k%29%2Fdk+=+100%289-144%2Fk%5E2%29.
Setting the derivative equal to 0,
+100%289-144%2Fk%5E2%29+=+0 ==> 9+-+144%2Fk%5E2+=+0 ==> 9+=+144%2Fk%5E2
==> k%5E2+=+144%2F9 ==> k = 4.
Now +d%5E2C%28k%29%2Fdk%5E2+=+100%28288%2Fk%5E3%29+%3E+0 when k = 4.
==> Absolute minimum at k = 4.
Minimum value is C(4) = 100(100 + 9*4 + 144/4) = 17,200 $.