Suppose Deskpro decides to sell $3$ computer models. Each one has the same holding cost of $$100$ per unit per annum. The first model has demand of $12,000$ per annum, the second one $1,200$ per annum and the last one $120$ units per annum. If Deskpro orders them together with a joint cycle time, then the company will save a huge sum of money. If replenished individually we have to pay $$4000$ per order for each item, however if replenished jointly in the same truck, we only pay $$7000$ for all three items.

a$)$ Find a joint cycle time for these three products and calculate total annual costs for procuring the three products jointly.

b$)$ Determine the EOQ and the annual costs for each of the three products if they are procured separately.

c$)$ Compare two procurement strategies in terms of costs.