A movie production company will be shooting on location in Atlanta, GA for five months. During this time period, the production company will require storage space for its sets, props and costumes, which it can lease from a local warehouse. The warehouse leases storage space by the square foot, at prices shown in Table $1$ below, depending on the duration of the lease. The warehouse will allow the production company to have multiple leases for space in any particular month and to lease space starting in any month for any duration. For example, the production company could sign a $3$ month lease for $30,000$ sq ft in month $1$ and then add $1$ month lease for an additional $20,000$ sq ft in month $3.$

Table $1$: Lease Cost

Cost Per Sq Ft Lease Duration

$$651$ month

$$1002$ months

$$1353$ months

$$1604$ months

$$1905$ months

The production company has varying needs for storage space over the course of the five month shoot. The space they estimate they will need in each month is shown in Table $2.$

Table $2$: Space Required

Month Sq Ft

$130,0006000$

$220,0004000$

$340,0008000$

$410,0002000$

$550,00010000$

$5$

Formulate and solve a LP model to determine the optimal leasing plan for the production company in order to have all the storage space it needs in each month at the minimum cost.

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