The JH logistics is trying to fulfill five orders(denoted as O) from two of its warehouse(denoted as W) to maximize its profit. The information about order quantities to be fulfilled, the warehouse capacities, and the profit margins ($/unit) for fulfilling each unit from each warehouse is summarized as follows:

Profit margin	O1	O2	O3	O4	O5	Capacity
W1	3.5	3.1	2.2	2.8	4.2	1500
W2	2.2	3.2	4	2.5	3.6	2400
Order quantity	900	750	660	1100	800

a) How many units should JH Logistics send from each warehouse to fulfill each order? You can assume that orders can be fulfilled in fractional numbers in this part. (4 points) Hint: It might be helpful to check the total capacity and the total order quantity before formulating the problem. Can all the orders be fulfilled? b) To be profitable to fulfill order 4 from warehouse 1, what should be the corresponding minimum profit margin? Justify your answer without resolving the problem. (2 points) c) Suppose there is a technology that can increase the capacity of warehouse 1 to 1650. How much is JH Logistics willing to pay for this technology at most? Justify your answer without re-solving the problem. (2 points) d)It is required that at least 28% of order 3 fulfilled by the two warehouses must come from warehouse1, Besides, no orders can be fulfilled in fractional numbers. Determine the profit-maximizing fulfillment plan by modifying your formulation in part a with these requirements. (2 points) Assume that the requirements in part d remain. In addition, order 5 cannot be fulfilled partially or separately from two warehouses. That is, the 800 units of order 5 should be fulfilled either all from warehouse 1 or all from warehouse 2. Otherwise, 0 units can be fulfilled by either warehouseDetermine the profit-maximizing fulfillment plan by modifying your formulation in part d with this additional requirement. (3 points)