Kyler Builders builds $1,500-$square$-$foot starter tract homes in the fast$-$growing suburbs of Atlanta. Land and labor are cheap, and competition among developers is fierce. The homes are a standard model, with any upgrades added by the buyer after the sale. Kyler Builders' costs per developed sublot are as follows:

$($Click the icon to view the costs.$)$

Kyler Builders would like to earn a profit of $14\%$ of the variable cost of each home sold. Similar homes offered by competing builders sell for $$208,000$ each. Assume the company has no fixed costs.

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Requirement $3.$ Bathrooms and kitchens are typically the most important selling features of a home. Kyler Builders could differentiate the homes by upgrading the bathrooms and kitchens. The upgrades would cost $$18,000$ per home but would enable Kyler Builders to increase the sales prices by $$31,500$ per home. $($Kitchen and bathroom upgrades typically add about $175\%$ of their cost to the value of any home.$)$ If Kyler Builders makes the upgrades, what will the new cost$-$plus price per home be$?$ Should the company differentiate its product in this manner?

Calculate the new cost$-$plus price per home.

Current variable cost per home

Plus: Variable cost of kitchen and bathroom upgrade per home

Total variable cost per home

Plus: Desired profit per home

Cost$-$plus price per home

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Data table

$\backslash$table$[[$Land$,$$$51,000$