Geoff Gullo owns a small firm that manufactures \"Gullo Sunglesses.\" He has the

Question

Geoff Gullo owns a small firm that manufactures "Gullo Sunglesses." He has the opportunity to sell a particular seasonal model to Land's End. Geoff offers Land's End two purchasing options:

Option 1. Geoff offers to set his price at $65 and agrees to credit Land's End $53 for each unit they return to Geoff at the end of the season. Since styles change each year, there is essentially no value in the returned merchandise.

Option 2. Geoff offers a price of $55 for each unit, but returns are no longer accepted. In this case, Land's End throws out unsold units at the end of the season.

This seasons demand for this model will be normally distributed with mean of 200 and standard deviation of 125. Land's End will sell those sunglasses for $100 each. Geoff's production cost is $25.

1) Suppose Land's End chooses option 2 and order 275 units. What are the Land's End's expected sales?

2) Suppose Land's End chooses option 2 and order 275 units. What are Land's End's expected leftover inventory?

Explanation / Answer

To maximize revenue, purchase 200 + 3 standard deviations to have enough to satisfy 99.7% of demand.

200 + 3(125) = 575 units

Option 1) 65 * 275 + 300 * 100

= 47,875

Option 2) 55 * 275 + 300 * 100

= 45,125

= 33,300

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