Application Problems
Serendipity: The three princes of Serendipity went on a little trip. They could not carry too much weight; More than 300 pounds made them hesitate. They planned to the ounce. When they returned to Ceylon, they discovered that their supplies were just about gone. When, what to their joy, Prince William found a pile of coconuts on the ground. "Each will bring 60 rupees," said Prince Richard with a grin, as he almost tripped over a lion skin. "Look out!" cried Prince Robert with glee, as he spied some more lion skins under a tree. "These are worth even more-300 rupees each if we can just carry them all down to the beach." Each skin weighed fifteen pounds and each coconut, five, but they carried them all and made it alive. The boat back to the island was very small 15 cubic feet baggage capacity-that was all. Each lion skin took up one cubic foot while eight coconuts the same space took with everything stowed they headed to sea and on the way calculated what their new wealth might be. "Eureka!" cried Prince Robert, "Our worth is so great that there’s no other way we could return in this state. Any other skins or nut that we might have brought would now have us poorer. And now I know what. I’ll write my friend Horace in England, for surely only he can appreciate our serendipity."
Formulate and solve Serendipity by graphical LP in order to calculate "what their new wealth might be."
Solution: Letbe the number of lion skins andbe the number of coconuts. The objective function is given by
We have the following restrictions:
- Weight:
- Boat Capacity:
This can be summarized as follows:
The feasible region is shown below:
There are 4 corners: (0, 0), (15, 0), (0, 60), (12, 24). We’ll see which one maximizes the objective function.
x |
y |
Objective |
0 |
0 |
0 |
15 |
0 |
4500 |
0 |
60 |
3600 |
12 |
24 |
5040 |
This means that they took 12 lion skins and 24 coconuts.