Your company is to decide on the number of trucks to be put on an annual $(4-$quarter$)$ lease for next year. If the company signs an annual lease, the annual leasing cost is $$6000$ per truck. If the company does not have enough trucks in a given quarter, it can also sign quarterly leases at a rate of $$700$ per truck

per quarter. The trucks leased annually require an average of $$300$ maintenance cost per truck per quarter $($only on quarters that the trucks are used$).$ Assume all other operational costs are the same for both annual and quarterly leases. The number of trucks needed in each of the next $4$ quarters are as follows:

Q$1$: $20$ trucks

Q$2$: $8$ trucks

Q$3$: $9$ trucks

Q$4$: $15$ trucks

How many trucks should be leased annually?