Show me the steps to solve $1.$ Michael and Barbara, business partners in a small marketing firm, began to budget for the next fiscal year. They felt comfortable with their sales budget and even their cost of services budget. The budget that generated the greatest amount of uncertainty for them was the administrative expenses budget. Michael did some digging into past invoices, labor costs, and other components of the overall expense category to determine what types of expenses were included in this line item. Here is what he gathered:

$$ For administrative labor, hours and costs varied by number of marketing projects and comprised approximately $70\%$ of the total administrative expenses. Administrative labor costs $$16/$hour$.$

$$ Office supplies costs seemed to occur at a steady rate regardless of the number of projects, representing $10\%$ of the total administrative expenses.

$$ Depreciation on the administrative equipment made up the remaining $20\%$ of total administrative expenses.

Barbara handled the payroll side of the small business, and he felt strongly that these administrative expenses rose and fell when administrative hours similarly rose and fell. This understanding was consistent with Michael's analysis as well. Barbara believed they could keep the analysis a bit more straightforward and simply calculate a cost evaluation using $1$ driver $$ administrative labor hours $$ and move forward with that.

Total administrative expenses for the past $8$ years, along with total administrative labor hours and a number of marketing projects, R as follows.

Using Michael's account analysis perspective, calculate the average number of administrative hours that were needed per project in the year just ended $($Year $8).$ Assuming no changes are expected for the fixed costs for next year, predict total administrative expenses if $33$ marketing projects are anticipated next year.