Josie's Place Inn, a proposed $30-$room motel with a fully equipped restaurant, will cost $\backslash (\backslash$$ $750,000\backslash )$ to construct. An estimated additional $\backslash (\backslash$$ $50,000\backslash )$ will be invested in the business as working capital. Of the total $\backslash (\backslash$$ $800,000\backslash )$ investment, $\backslash (\backslash$$ $400,000\backslash )$ is to be secured from the Columbo Federal Bank at the rate of $10$ percent interest. The projected occupancy rate is $80$ percent for the year. The owners desire a $15$ percent return on equity after the corporation pays income taxes of $25$ percent. The estimated undistributable expenses, not including income taxes and interest expense, total $\backslash (\backslash$$ $480,000\backslash ).$ The estimated direct expenses of the rooms department are $\backslash (\backslash$$ $7\backslash )$ for each room sold. Consider a year to have $365$ days. Required: $1.$ Determine the average price of a room using the Hubbart Formula, assuming the contribution from the restaurant department is $\backslash (\backslash$$ $0\backslash ).2.$ If the double rooms are sold at a premium of $\backslash (\backslash$$ $10\backslash )$ over singles$,$ what is the price of singles and doubles? Assume a double occupancy rate of $40$ percent. $3.$ If the restaurant generates a department profit of $\backslash (\backslash$$ $20,000\backslash )$ per year, how much may average room rates be decreased and still meet the owners' financial goals?