Answer:
$4,265.90
Explanation:
-Let X and Y be the two sides of the rectangle and C be the cost function.
-The cost function can then be expressed as:
C=25(2y+x)+10x
C=50y+35x ...(i)
#The region's area is equated as:
xy=2600 ...(ii)
#We make Y the subject of the formula in i and substitute in ii;
y=2600/x
=>C=50y+35x
C=50(2600/x)+35x
C=130000/x+35x
#We get the first derivative to determine the critical points:
dC/dx=-130000/x^2+35
#Set dC/dx=0
130000/x^2=35
x=60.94 ft
y=2600/x=2600/60.94=42.66 ft
-The minumum is therefore calculated as:
C=50y+35x
=50(42.66)+35(60.94)
=$4,265.90
Hence, the minimum cost is $4,265.90