(Answer in Excel sheet )

You have been hired by Faraday Protonic Company (FPC) to serve as their Pellet Transshipment Manager. Faraday Protonic is a joint public-private energy company dedicated to generating clean and safe nuclear energy. FPC uses a new technology based on radioactive pellets. These pellets can generate electricity for years in FPC's nuclear plants. Once the radioactive pellets are depleted, they are removed from active use and collected at the plants for removal at the end of the month. Once a month, the depleted pellets are removed from the plants, transported to an inspection site for examination, and then moved again to a dedicated storage site for safekeeping.

You have been informed that two of FPC's nuclear plants, called Plant One and Plant Two, need to move out depleted pellets in the following amounts:

- Plant One wants to ship out up to 83 pellets per month
- Plant Two wants to ship out up to 127 pellets per month

This is how many pellets these two plants want to ship out per month. However, the exact number of pellets that will actually be moved out from each plant depends on the space that is available at the dedicated storage sites that would ultimately receive them. FPC is mandated by law to move as many pellets out of the plants as the storage sites are able to receive. You have been informed that two of FPC's dedicated storage sites, called Storage X and Storage Y, are ready to receive depleted pellets from FPC's plants, in the following amounts:

- Storage X is ready to receive a total of 97 pellets per month
- Storage Y is ready to receive a total of 101 pellets per month

Since the two plants want to ship out more pellets per month than the two storage sites can receive, you know that some pellets will have to stay in their plant of origin until a later time. This is not a problem, however, since every one of FPC's plants has the capacity to temporarily store whatever pellets are not shipped out, and the law allows this.

At this time, only one inspection site is available to receive the pellets from the two plants, inspect them, and send them out to the two storage sites. It is called Inspection Site A. Notice that inspection sites do not have storage capacity: the pellets come in, are inspected, and continue their trip to the storage sites.

Moving radioactive material is not easy and therefore it is not cheap either. There is a lot of planning and security involved. Each shipment of pellets has to be closely monitored and protected to prevent the loss of radioactive material. Also, the vehicles transporting the material have to move relatively slowly, to avoid accidents. Therefore, it is very expensive to transport the radioactive pellets from the plant to the inspection site, and from there to the storage site. Based on estimates and historical data, FPC has calculated the following transportation costs, in dollars per pellet moved:

- It costs 7.33 dollars to move one pellet from Plant One to Inspection Site A
- It costs 9.29 dollars to move one pellet from Plant Two to Inspection Site A
- It costs 3.49 dollars to move one pellet from Inspection Site A to Storage X
- It costs 9.41 dollars to move one pellet from Inspection Site A to Storage Y

You decide to optimize the transshipment of depleted pellets from the plants to the storage sites (stopping on the way at Inspection Site A, of course) in order to minimize the overall monthly transportation cost. In this optimized solution, how many pellets will Plant Two be able to ship out to the Inspection Site A every month? (This question is not graded.)

Part 1

(1 point possible)

In this optimized solution, how much is the overall monthly transportation cost for FPC? (This question is graded.) Give your answer in dollars, without typing in the box a dollar sign or comma. For example, if your answer is $1,234, type 1234 in the box. Hint: The answer is more than 2000 but less than 4000.

Part 2

(1 point possible)

FPC has calculated the following transportation costs for Inspection Site B, in dollars per pellet moved:

- It costs 6.59 dollars to move one pellet from Plant One to Inspection Site B
- It costs 8.87 dollars to move one pellet from Plant Two to Inspection Site B
- It costs 4.63 dollars to move one pellet from Inspection Site B to Storage X
- It costs 8.77 dollars to move one pellet from Inspection Site B to Storage Y

As before, you will optimize the transshipment of depleted pellets from the plants to the storage sites, stopping first at the inspection sites, so as to minimize the overall monthly transportation cost. How much will this cost FPC every month? (This question is graded.) Give your answer in dollars, without typing in the box a dollar sign or comma. For example, if your answer is $1,234, type 1234 in the box. Hint: In this optimal solution, Plant Two ships a total of 18 pellets per month to Inspection Site B.

You have just received two e-mails from your boss. The first informs you that a third nuclear plant, called Plant Three, is ready to move out up to 179 depleted pellets per month. The second tells you that a third dedicated storage site, called Storage Z, is ready to receive a total of 103 depleted pellets per month from FPC's plants. FPC has calculated the following transportation costs for the new plant and storage site, in dollars per pellet moved:

- It costs 9.11 dollars to move one pellet from Plant Three to Inspection Site A
- It costs 5.41 dollars to move one pellet from Plant Three to Inspection Site B
- It costs 8.81 dollars to move one pellet from Inspection Site A to Storage Z
- It costs 8.63 dollars to move one pellet from Inspection Site B to Storage Z

Again you will optimize the transshipment of depleted pellets from the three plants to the three storage sites, stopping first at the inspection site, so as to minimize the overall monthly transportation cost. In this optimal solution, how many pellets is Plant One sending to Inspection Site B? (This question is not graded.)

Part 3

(1 point possible)

In this optimized solution, how much is the overall monthly transportation cost for FPC? (This question is graded.) Give your answer in dollars, without typing in the box a dollar sign or comma. For example, if your answer is $1,234, type 1234 in the box. Hint: The answer is more than 3000 but less than 5000.

Part 4

(2 points possible)

FPC has learned that a new regulation, to be enacted soon, will require that no depleted pellets be stored at the plants past the monthly removal date. To acomodate this, the storage sites have increased the total number of pellets they are willing to receive every month, as follows:

- Storage X is now ready to receive a total of 130 pellets per month
- Storage Y is now ready to receive a total of 129 pellets per month
- Storage Z is now ready to receive a total of 130 pellets per month

The new regulations also make it easier for pellets to be moved, which reduces all the transportation costs in the network by 3.13 percent. (This means you have to multiply all the previous transportation costs by 0.9687 in order to get the new costs.) One last time, you will optimize the transshipment of depleted pellets from the three plants to the three storage sites, stopping first at the inspection sites, so as to minimize the overall monthly transportation cost. (Hint: In this optimized solution, Plant One is shipping 3 pellets per month to Inspection Site A.)

In this optimized solution, how much is the overall monthly transportation cost for FPC? (This question is graded, and worth 2 points.) Give your answer in dollars, without typing in the box a dollar sign or comma. For example, if your answer is $1,234, type 1234 in the box.

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