2. A clothing manufacturer in Colombia regularly ships products to the US. There
ID: 396571 • Letter: 2
Question
2. A clothing manufacturer in Colombia regularly ships products to the US. There is a fixed cost for each shipment of $1000, plus a transportation cost that depends on the shipment size, as shown in the table below. The US demand for the products averages 2,000 pounds per week. Shipment size 7,500 lbs Rate in S/cwt 600 500 400 (5 pts.) a) If shipments of 2,000 pounds are sent every week from the Colombian manufacturer to the US, then what would be the annual cost? (8 pts.)b) Suppose the Colombian manufacturer was to send a shipment every four weeks (rather than shipping every week as in part a). This may reduce transportation costs, but it incurs an additional inventory cost of $1.00 per pound for each week products are delayed and held by the manufacturer. What would be the total annual cost if the manufacturer ships four times as much every four weeks? (7 pts.)c) Now suppose the Colombian manufacturer was to send a shipment every three weeks (not as in part a or part b). However, the inventory cost is not known (it is not $1.00 per pound per week as in part b). How large can the inventory cost be in S per pound for each week delayed if the total cost to ship every three weeks is equal to $11,000 per week?Explanation / Answer
Each shipment cost = $1000
US demand : 2000 lbs/ week
a) The cost of sending 2000 lbs (20 cwt ) every week= fixed shipment charge + charge per weight
= $1000 + (20*600) = $1000 + $12000 = $13,000
Now the annual cost or the cost for 52 weeks = 52 *13000 = $676,000 (Answer a)
b) The cost of sending 8000 lbs (80 cwt ) in every 4 weeks = fixed shipment charge + charge per weight + inventory cost w.r.t weight and inventory held
= $1000 + (80*400) + ($3*2000lbs + $2*2000lbs + $1*2000lbs) = $1,000 + $32,000 + 12,000= $45,000
Now the annual cost or the cost for 52 weeks = 13*45000 = $585,000 (Answer b)
c) The cost of sending 6000 lbs (60 cwt ) in every 3 weeks = fixed shipment charge + charge per weight + inventory cost w.r.t weight and inventory held. Taking the inventory cost as ‘x’. and total cost for 3 weeks is 3*$11,000= $33,000
= $1000 + (60*500) + ($x*2*2000lbs + $x*1*2000lbs) = $1,000 + $30,000 + 6,000*x = $33,000
= 31,000+6,000*x = 33,000
X = 2,000/6,000
Now the inventory cost per pound = $0.33 per pound of weight (Answer c)
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