Professor Mittman smiled again and gazed wistfully into the distance as he considered the numbers in front of him:
The back-to-school season lasts 12 weeks, starting when students return in August. Geocoins are only sold during this period, and there is no possiblity to reorder during the sales season. The 1,000 bronze geocoins and 100 silver geocoins each have separate price points. At the beginning of each week, there will be a chance to possibly reset the price of the geocoins for the week (depending on the stock level at the time and the number of weeks left in the selling season). As is typical in retail sales, the price can never increase from the previous week's price. At the end of the 12-week sales season, any remaining geocoins will be melted down for scrap. He estimates at that point the value of each scrapped bronze coin will be $0.50 and each silver coin will be $8.
Professor Mittman had the previous night assembled a team of PhD candidates to determine market conditions for geocoins in Central New York. 27 Red Bulls and 5 Dominoes pizzas later, the the students offered the following charts, which show how many geocoins they expect to sell per week at each sales price:
Bronze Geocoin Pricing and Revenues
(1000 total for sale, $0.50 scrap value)
230 per week at $5.96 = $1,370 per week
220 per week at $6.33 = $1,393 per week
175 per week at $6.83 = $1,195 per week
90 per week at $7.88 = $709 per week
70 per week at $8.24 = $577 per week
50 per week at $9.36 = $468 per week
Silver Geocoin Pricing and Revenues
(100 total for sale, $8 scrap value)
17 per week at $16.65 = $283 per week
15 per week at $18.80 = $282 per week
13 per week at $21.15 = $275 per week
9 per week at $23.67 = $213 per week
7 per week at $27.29 = $191 per week
5 per week at $32.80 = $164 per week
Before rushing out the door with GPS units in hand, the students mentioned that these numbers are very certain, and that the sales of one coin will not affect the other (ie, the bronze geocoin buyer will be unaffected by how much the silver geocoin costs).
Professor Mittman wants to set the optimal price for each week now so that he can spend the rest of the year geocaching (and not have to worry about monitoring sales). For him, this is a simplex matter to solver. He will set the price to one of these recommended price levels every week for the 12-week back-to-school period (as constrained above) in order to optimize his expected revenue for each geocoin.
He had the previous week consulted a colleague in Marketing to develop a strategy to promote the coins. Following her advice, Professor Mittman left a geocache hidden in the area around the Whitman School of Management to help publicize geocaching. Its location depends on the optimal expected revenue for each of the two series of geocoins:
N 43 X, W 076 Y, where:
X = Optimal 12-week expected revenue for silver geocoins / 1,000
Y = Optimal 12-week expected revenue for bronze geocoins / 1,000
As Professor Mittman unsheathed his price gun, he wondered whether any of his students would be able to find the geocache before the start of classes.
