A pharmaceutical company, named “LongerLife”, plans to deliver clinical trials to three different clinics (C1, C2, and C3). The trials are used for the emergency treatments so LongerLife must fulfill all requirements. LongerLife has 3 deliver trucks. Each truck can ship 200 trials per trip. Depending on the distance between LongerLife and its clinics, the shipping cost may be different. Usually, it takes a week to deliver, i.e., if we decide to deliver in Week 1, the clinic will receive the trials in Week 2 and the truck will be available in Week 2. Each clinic has a dedicated space for holding the left-over trials. The holding cost per trial is around ten cents per week. To simplify the question, LongerLife can produce as many trials as we want in any week. Currently, LongerLife just delivers the trails when the clinics don’t have any inventory on hand. Due to the high shipping cost and the frequent out of stocks, LongerLife requests our help. The company has provided the following data. Please use the optimization skills and help LongerLife improve the distribution plan.
The demand data is as follows.
Weeks    1 2 3 4 5 6 7 8 9 10
C1            0 0 220 70 60 150 30 130 60 60
C2            0 150 30 50 50 10 450 100 50 90
C3            0 50 160 40 200 170 0 30 30 120
The shipping cost may depend on the distance. The following data is the shipping cost per round trip.
                                             C1    C2       C3
Shipping cost per round    150   200      250
The space in the clinics is shown in the following table.
                                        C1       C2       C3
Inventory Limitation       225    150    100

Please provide a report to manager that answers the following:
I. Formulate the problem to determine the distribution in order to minimize the total cost. Please provide a mathematical description of the model and solve.

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