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Windsor Company estimates that unit sales will be $10,300$ in quarter $1$;$11,500$ in quarter $2$;$14,400$ in quarter $3$ ; and $18\mathrm{.}500$ in quarter $4.$ Management wants to have an ending finished goods inventory equal to $20\%$ of the next quarter's expected unit sales. Prepare a production budget by quarters for the first six months of $2022.$