The table below provides shipping rates for packages using UPS next day air or g

Question

The table below provides shipping rates for packages using UPS next day air or ground service options. The rates vary according to both the weight of the package and the distance of the shipment (larger numbered zones are farther away). Note that the zone number also indicates the number of days required to deliver a package using ground service. For example, it would take three days and cost $7.40 to send a 10-pound package to zone 3 using ground service.

Suppose you have a package weighing 10 pounds that needs to be shipped to zone 3. The value of the material is $13,000 and the annual inventory holding rate is 35 percent of the product value.

a-1. Calculate the total shipping and transit inventory cost using the air and ground transportations. (Use 365 days in a year. Do not round intermediate calculations. Round your answers to 2 decimal places.)

a-2. Which transportation mode (air or ground) minimizes the total shipping and transit inventory cost? (Round your answer to 2 decimal places.)

b. How high would the inventory holding rate have to be in order to justify next day air service? (Use 365 days in a year. Do not round intermediate calculations. Round up your answer to the next whole number.)

Table of Shipping Rates Next Day Service Weight Domestic Zones 1 2 3 4 5 6 7 1 Lbs. $ 16.25 $ 19.25 $ 22.75 $ 24.75 $ 27.00 $ 28.25 $ 29.00 2 $ 17.25 $ 20.75 $ 25.50 $ 27.75 $ 30.25 $ 31.25 $ 32.00 3 $ 19.00 $ 21.75 $ 28.25 $ 30.50 $ 33.50 $ 34.75 $ 35.50 4 $ 20.00 $ 22.75 $ 31.00 $ 33.50 $ 36.50 $ 37.75 $ 38.50 5 $ 21.25 $ 24.25 $ 33.50 $ 36.25 $ 39.50 $ 40.75 $ 41.75 6 $ 22.00 $ 25.25 $ 36.00 $ 39.00 $ 42.75 $ 44.00 $ 45.00 7 $ 22.75 $ 27.00 $ 38.50 $ 42.00 $ 46.00 $ 47.00 $ 48.25 8 $ 23.75 $ 28.25 $ 41.00 $ 44.75 $ 49.25 $ 50.25 $ 51.25 9 $ 24.50 $ 29.75 $ 43.75 $ 47.50 $ 52.50 $ 53.75 $ 54.50 10 $ 25.25 $ 31.00 $ 46.25 $ 50.25 $ 55.25 $ 56.75 $ 57.75 11 $ 26.25 $ 32.50 $ 48.75 $ 52.75 $ 58.00 $ 60.00 $ 60.75 12 $ 27.00 $ 33.50 $ 51.25 $ 55.50 $ 60.75 $ 63.00 $ 63.75 13 $ 27.75 $ 34.75 $ 53.75 $ 58.00 $ 63.25 $ 65.75 $ 66.50 14 $ 28.50 $ 36.00 $ 55.75 $ 60.50 $ 65.75 $ 68.50 $ 69.25 15 $ 29.50 $ 37.50 $ 58.00 $ 63.00 $ 68.25 $ 70.75 $ 72.00

Explanation / Answer

a-1

Total cost = In-transit inventory holding cost + Carrier cost

or, Total cost for air freight = ((1/365) x $13,000 x 35%) + $46.25 = $58.72

and Total cost for ground service = ((3/365) x $13,000 x 35%) + $7.4 = $44.79

a-2

Ground service minimizes the cost by $58.72 - $44.79 = $13.92

a-3

Let 'h' be the rate, so that

((1/365) x $13,000 x h/100) + $46.25 = ((3/365) x $13,000 x h/100) + $7.4 = $36.17

or, 130h/365 + 46.25 = 390h/365 + 7.4

or, 260h/365 = 38.85

or, h = 54.54% or 54.54%

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