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 dont 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 trip($)	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: 1. Formulate the LP to determine the distribution in order to minimize the total cost. Please provide a mathematical description and MPL code of the probelm.

Please include constraints and description of the model.