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Chapter 4, Problem 60RE
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### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

#### Solutions

Chapter
Section
BuyFindarrow_forward

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Inventory Cost The cost of inventory C depends on the ordering and storage costs according to the inventory model C = ( Q x ) s + ( x 2 ) r Determine the order size that will minimize the cost, assuming that sales occur at a constant rate, Q is the number of units sold per year, r is the cost of storing one unit for one year, s is the cost of placing an order, and x is the number of units per order.

To determine

To calculate: The size of an order that minimizes the cost where cost of inventory is C=(Qx)s+(x2)r

Explanation

Given:

The cost function, C, for x units per order, where Q gives the number of units sold, s is the cost incurred to place the order and r is the cost incurred to store the order.

C=(Qx)s+(x2)r

Formula Used:

For a function f that is twice differentiable on an open interval I, if f'(c)=0 for some c, then,

If f''(c)>0 the function f has relative minima at c if f''(c)<0 the function f has relative maxima at c. If f''(c)=0, the test fails.

Calculation:

The quantity to be minimized, or the primary equation would be:

C=(Qx)s+(x2)r

Here as x is number of units for a single order, the feasible domain is:

0<x<âˆž

Differentiate the equation obtained and equate it to zero to obtain,

(âˆ’Qsx<

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