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

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 : , 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) (Show Source): You can put this solution on YOUR website!
C(1) = 100(100 + 9 + 144) = 25,300 $ total cost of storage and transportation.
==> .
Setting the derivative equal to 0,
==> ==>
==> ==> k = 4.
Now when k = 4.
==> Absolute minimum at k = 4.
Minimum value is C(4) = 100(100 + 9*4 + 144/4) = 17,200 $.

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