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United States Motors Incorporated $($USMI$)$ manufactures automobiles and light trucks and distributes them for sale to consumers through franchised retail outlets. As part of the franchise agreement, dealerships must provide monthly financial statements following the USMI accounting procedures manual. USMI has developed the following financial profile of an average dealership that sells $3,300$ new vehicles annually:

AVERAGE DEALERSHIP FINANCIAL PROFILE

Composite Income Statement

Sales $ $66,000,000$

Cost of goods sold $54,450,000$

Gross profit $ $11,550,000$

Operating costs

Variable $1,897,500$

Mixed $5,082,000$

Fixed $4,078,800$

Operating income $ $491,700$

USMI is considering a major expansion of its dealership network. The vice president of marketing has asked Jack Snyder, corporate controller, to develop some measure of the risk associated with the addition of these franchises. Jack estimates that $90\%$ of the mixed costs shown are variable for purposes of this analysis. He also suggests performing regression analyses on the various components of the mixed costs to more definitively determine their variability.

Required:

$1.$ Calculate the composite dealership profit if $4,700$ units are sold.

$3.$ The regression equation that Jack Snyder developed to project annual sales of a dealership has an R$-$squared of $60\%$ and a standard error of the estimate of $$9,900,000.$ If the projected annual sales for a dealership total $$62,700,000,$ determine the approximate $95\%$ confidence interval for Jack$$s prediction of sales. $($Hint: The $95\%$ confidence interval uses $2$ standard errors in determining the interval.$)$

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