Ukulelor
Ted, is running a business in the music industry, a ukulele factory. His brand, Ukulelor, is becoming a big success because of the excellent quality of the ukuleles that he produces and the recent marketing investment that Ted has made.
Every week, Ted ships all his production to seven major partner retailers. But, recently, the demand has been increasing tremendously to the point that Ted has not been able to keep up with the production. Since Ted is not allowed to increase prices due to contractual reasons, he must decide how much to fulfill each order that he receives every week.
The table shows the data from last week when the factory was able to produce and ship 650 ukuleles, 510 below the total demand which was 1,160.
| Retailer ID | Wholesale Unit Price ($) | Order Qty. | Shipped Qty. |
|---|---|---|---|
| R1 | 47.00 | 230 | 50 |
| R2 | 65.00 | 150 | 135 |
| R3 | 70.00 | 270 | 270 |
| R4 | 68.00 | 90 | 90 |
| R5 | 46.00 | 190 | 0 |
| R6 | 78.00 | 55 | 55 |
| R7 | 55.00 | 120 | 50 |
To arrive at the numbers you see in the last column, Ted got help from Mr. Mip.
At first, these numbers might sound unreasonable. You would probably expect to see the order from R2 being met in whole and the order from R1 not being fulfilled at all. That would be the case if the only goal were to maximize profit. In this case, Mr. Mip could have simply sorted the retailers by selling price and fulfilled first the orders with higher prices.
However, Ted has a contract signed with each retailer. And one of the agreements in the contract is that Ted incurs a fee of 20 times the wholesale price of a ukulele if he can’t ship at least 50 ukuleles to a retailer that placed an order for that week.
How did Mr. Mip arrive at those numbers?