This example deals with a discrete optimization problem of determining the most economical amountof attic insulation for a large single$-$story home in Virginia. In general, the heat lost through the roofof a single$-$story home isIn southwest Virginia, the number of heating days per year is approximately $230,$ and the annualheating degree$-$days equals $230(65$oF$46$oF$)=4,370$ degree days per year. Here, $65$oF is assumed tobe the average inside temperature and $46$oF is the average outside temperature each day.Consider a $2,400-$ft$2$ single$-$story house in Blacksburg. The typical annual space$-$heating load for thissize of a house is $100\backslash$times $106$ Btu. That is$,$ with no insulation in the attic, we lose about $100\backslash$times $106$ Btuper year. Common sense dictates that the no insulation alternative is not attractive and is to beavoided.Page $2$ of $2$With insulation in the attic, the amount of heat lost each year will be reduced. The value of energysavings that results from adding insulation and reducing heat loss is dependent on what type ofresidential heating furnace is installed. For this example, we assume that an electrical resistancefurnace is installed by the builder, and its efficiency is near $100\%.$Now were in a position to answer the following question: What amount of insulation is mosteconomical? An additional piece of data we need involves the cost of electricity, which is $$0\mathrm{.}074$ perkWh. This can be converted to dollars per $106$ Btu as follows $(1$ kWh $=3,413$ Btu$)$:The cost of several insulation alternatives and associated space$-$heating loads for this house are givenin the following table $($an R$-$value indicates the resistance to heat transferthe higher the numberthe less the heat transfer$)$: