A domestic producer of baby carriages, Pramble must deliver di units of baby carriages at the end of the ith month (for i= 1,..5, di values are given in the following table). Baby carriages can be produced for $ 100 and can be delivered at the end of the same month or stored as inventory and delivered at the end of the following month; however, there is a $ 5 monthly storage cost for each unit of baby carriages kept in inventory. At the beginning of month 1, 3 baby carriages are available. If Pramble produces xi units in month i and xi+1 units in month i +1, it incurs a cost of 40|xi+1 xi| dollars, reflecting the cost of switching to a new production level. Formulate a linear programming problem aimed at minimizing the total cost of production and inventory plan over a five-month period. Suppose the inventory remaining at the end of 5th month has no value and does not incur any storage costs. 5 Months di 1 15 2 17 3 19 4 11 a) (10 pts) Formulate an NLP to minimize the total cost of the company to meet all the demand at the end of 5 months. b) (10 pts) Linearize the NLP you formulated in part a. You may define extra decision variables if you need