The heating and cooling costs for an uninsulated building are $850,000 per year.
ID: 2829915 • Letter: T
Question
The heating and cooling costs for an uninsulated building are $850,000 per year. If x inches (x< 9) of insulation are added, the combined heating and cooling costs with be 2,550,000/(x+3) dollars per year. Assume that it costs $200,000 for each inch (thickness) of insulation added.
A) How many inches of insulation should be added in order to minimize total costs (insulated cost + combined heating and cooling costs) over a 5-year period?
B) If the number of inches of insulation added must be a whole number, how many inches should be added in order to minimize the total cost?
Explanation / Answer
a)
C = 2,550,000/(x+3) + 200000x
should be minimum
=>
dC/dx = 0
=>
-2550000*5/(x+3)^2 +200000 = 0
=>
(x+3)^2 = 2550*5/200
=>
x = 5.98 inches
(b) number of inches = 6
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