Question 288373
A fence is to be built to enclose a rectangular area of 290 square feet.
 The fence along three sides is to be made of material that costs 4 dollars per foot, 
and the material for the fourth side costs 15 dollars per foot.
 Find the length L and width W (with W \leq L) of the enclosure that is most economical to construct.
:
Area equation:
L * W = 290
W = {{{290/L}}}
:
Perimeter equation
P = 2L + 2W
:
Cost to enclose
C = 4(2L) + 4W + 15W
C = 8L + 19W
Replace W with {{{(290/L)}}}
C = 8L + 19{{{(290/L)}}}
C = 8L + {{{5510/L}}}
:
Plot this equation, L is on the x axis, Cost on the y axis
{{{ graph( 300, 200, -10, 40, -200, 1000, 8x+(5510/x)) }}} 
Minimum cost when L = 26 ft
then
{{{290/26}}} ~ 11.15 ft is the width
:
Check area: 26 * 11.15 = 289.9 ~ 290
Check cost: 4(2*26) + 4(11.15) + 15(11.15) = $419.85 is minimum cost