Green Valley Gardens $($GVG$)$ is a small floral shop in a suburban town. They specialize in creating custom floral arrangements for various occasions. The time required to assemble one floral arrangement is $30$ minutes, and the cost per arrangement is $$50.$ GVG employs four florists, each working eight$-$hour shifts, five days a week $($assume four weeks per month$).$ The estimated demand for the next five months is as follows:

$$ Month $1$: $10$ arrangements

$$ Month $2$: $15$ arrangements

$$ Month $3$: $5$ arrangements

$$ Month $4$: $20$ arrangements

$$ Month $5$: $7$ arrangements

GVG wants to maintain a minimum of three arrangements in inventory at all times. The current inventory is five arrangements. The inventory holding cost is $15\%$ of the production cost.

Therefore, the inventory holding cost is $($$$50)(0\mathrm{.}15)=$$$7\mathrm{.}5.$ Create and solve an optimization model to determine the optimal number of floral arrangements to assemble each month, aiming to minimize the total cost while meeting the expected demand.