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Collingwood Contractors $($CC$)$ designs and builds new model homes for individual customers. CC has developed a reputation in the market for relatively upscale, unique designs with high$-$end finishings. CC has developed several formulas, which it uses to estimate costs and provide price quotes for prospective buyers. These include costs for materials, labor, and other resources. Although multiple configurations are possible for any house, CC uses three levels $($or tiers$)$ to represent increasing levels of luxury in terms of materials used. In addition, the customer can choose among three levels of increasingly sophisticated appliances and other house equipment. Finally, there is cost to bring utilities $($electricity$,$ water, and so on$)$ to the house if required. Of course, these estimates are dependent on the region of the country and whether the lot is located in a city or in a suburb or rural area. If the building site is in a city, a premium is added based on the building and equipment costs. The following are the cost estimates for one region in the Northwest:

Design and administrative costs $ $35,000$

Building costs per square foot $($Tier I$)110$

Building costs per square foot $($Tier II$)180$

Building costs per square foot $($Tier III$)235$

Equipment $($appliances$,$ and so on$)--$ Ruby $18,000$

Equipment $($appliances$,$ and so on$)--$ Sapphire $27,000$

Equipment $($appliances$,$ and so on$)--$ Emerald $36,000$

Utilities required? If yes, $...39,000$

City premium $($applied to building and equipment costs$)15\%$

Required:

A customer has expressed interest in having CC build a Tier III, $4,500-$square$-$foot home. The building site is a city lot and the customer wants the Sapphire level equipment. Based on the engineering estimates above, what will such a house cost to build? No additional utilities access is required.

Another customer has expressed interest in having CC build a smaller, Tier I, home, but with emerald$-$level equipment. This home will be on a vacant lot in the country and require utilities access to be added. The customer has chosen a $2,200-$square$-$foot design. Based on the engineering estimates above, what will such a house cost to build?

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