Power Brokers, Inc. $($PBI$),$ a discount brokerage firm, is contemplating opening a new regional office in Providence, Rhode Island. An accounting cost analysis of monthly operating costs at a dozen of its regional outlets reveals average fixed costs of $$4,500$ per month and average variable costs of AV C $=$ $$59$ $$0\mathrm{.}006$Q where AV C is average variable costs $($in dollars$)$ and Q is output measured by number of stock and bond trades. A typical stock or bond trade results in $$100$ gross commission income, with PBI paying $35\%$ of this amount to its sales representatives $($i$.$e$.,$ this payment $$leaves$$ the office$).$ Do not use derivatives. Be sure to show your work. $($a$)$ Estimate the trade volume necessary for PBI to break even on a monthly basis at a typical office. $($b$)$ Estimate the trade volume necessary for PBI to reach a target return of $$7,500$ per month for a typical office.