Question

Please answer now, 50 points!

A retailer has determined that the cost of ordering and storing X units is given by the equation C= 7x + (210,000 / x) where 1 ≤ X ≤ 100
The truck that transports them can carry at most 100 units. what is the number of units that must be ordered to minimize the cost

Answer 1

Answer:C' = 7-230000/x^2

Explanation:

Min occurs when C'=0

0=7-230000/x^2

230000/x^2=7

230000=7x^2

32857.128 = x^2

181.265 = x

Out of range.

So the min must be at an endpoint.

C(1) = 7+230000 = 230007

C(100) = 700+2300 = 3000

Since C(100)<C(1), C(100) is the minimum on the interval [1, 100]

The order size that will minimize cost is 100 units.