Star a retailer of mechanical tools sells three models of Instruments A, B &C. Annual demands for the three products are 10,000 for A, 2,000 for B and 30 for C. Cost is as follows - A costs $600, B $850 and C $2,000. The shipping cost of $5,000 for every order. For every model ordered and delivered, an additional fixed cost of $1,000 is incurred for receiving and storage. Star uses an annual holding cost rate of 20%. STAR is considering different strategies regarding the replenishment of these three models.

1) Case 1 Find the optimal order quantity and the average annual total cost associated with for all three items if each model is ordered and delivered independently which means a separate vehicle delivers each model.

2) Case 2 Find the optimal order quantities and the average annual total cost if all three models are ordered jointly (this means all models are ordered at the same time and thus, every order placed contains quantities of each of the three models).

3) Case 3 In this case , 2 of the items are ordered jointly and one is ordered independently. For instance A and B can be ordered jointly and C independently. There will be 3 different combinations of this strategy that needs to be considered. Calculate the optimal order quantities and then the average total annual costs for all the cases.