The Harvard Co-op orders sweatshirts with the Harvard University emblem on them and sells them for $50 each. During a typical month, 900 sweatshirts are sold (this includes all styles and sizes ordered from a partic-ular supplier). It costs $25 to place an order (for multi-ple sizes and styles) and 25 percent to carry sweatshirts in inventory for a year.
a. How many sweatshirts should the Co-op order at one time?
b. The supplier would like to deliver sweatshirts once a week. How much will this cost the Co-op per year? Under what conditions would you agree to the sup-plier's proposal?
c. Suppose that sales increase to 1500 sweatshirts per month but you decide to keep the lot size the same as in part a How much will this decision cost the Co-op per year?
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Harvard Co-op orders sweatshirts
a. How many sweatshirts should the Co-op order at one time?
The Harvard Co-op should order 1,200 sweatshirts at one time. This is the optimal lot size, which is found by setting the carrying cost equal to the ordering cost.
The carrying cost per sweatshirt is 25% * $50 = $12.50.
The ordering cost is $25 per order.
So, we set up the following equation:
$12.50 * Q = $25
$Q = 2
Therefore, the optimal lot size is Q = 2, or 1,200 sweatshirts.
b. The supplier would like to deliver sweatshirts once a week. How much will this cost the Co-op per year? Under what conditions would you agree to the supplier's proposal?
If the supplier delivers sweatshirts once a week, the Co-op will incur an additional carrying cost of $12.50 * 52 = $650 per year.
The Co-op would agree to the supplier's proposal if the additional carrying cost is less than the cost savings of not having to place as many orders.
For example, if the Co-op currently places 12 orders per year, the cost savings would be 12 * $25 = $300.
Therefore, the Co-op would agree to the supplier's proposal if the additional carrying cost is less than $300.
c. Suppose that sales increase to 1500 sweatshirts per month but you decide to keep the lot size the same as in part a. How much will this decision cost the Co-op per year?
If sales increase to 1,500 sweatshirts per month, the Co-op will incur an additional carrying cost of $12.50 * 1,500 = $1875 per year.
The total cost of carrying sweatshirts will be $1875 + $650 = $2525 per year.
This decision will cost the Co-op an additional $2525 per year.
The Co-op should only make this decision if the additional sales revenue is greater than the additional carrying cost.
For example, if the additional sales revenue is $3,000 per year, then the decision would be profitable.
Sample Solution
The Harvard Co-op should order 1,200 sweatshirts at one time. This is the optimal lot size, which is found by setting the carrying cost equal to the ordering cost.Our Services
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