Solved: Inventory Replenishment The ordering and transportation cost for the components

Chapter 3, Problem 91

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Inventory Replenishment The ordering and transportation cost C for the components used in manufacturing a product is \(C=100\left(\frac{200}{x^{2}}+\frac{x}{x+30}\right), \quad x \geq 1/) where C is measured in thousands of dollars and x is the order size in hundreds. Find the rate of change of C with respect to x when \(\text { (a) } x=10 \text {, (b) } x=15 \text {, and (c) } x=20\). What do these rates of change imply about increasing order size?

 

Text Transcription:

C=100(200/x^2+x/x+30), x geq 1

(a) x=10, (b) x=15 , and (c) x=20