Respuesta :
Answer:
Dimensions of the rectangular plot will be 500 ft by 750 ft.
Step-by-step explanation:
Let the length of the rectangular plot = x ft.
and the width of the plot = y ft.
Cost to fence the length at the cost $3.00 per feet = 3x
Cost to fence the width of the cost $2.00 per feet = 2y
Total cost to fence all sides of rectangular plot = 2(3x + 2y)
2(3x + 2y) = 6,000
3x + 2y = 3,000 ----------(1)
3x + 2y = 3000
2y = 3000 - 3x
y = [tex]\frac{1}{2}[3000-3x][/tex]
y = 1500 - [tex]\frac{3x}{2}[/tex]
Now area of the rectangle A = xy square feet
A = x[[tex]1500-\frac{3x}{2}[/tex]]
For maximum area [tex]\frac{dA}{dx}=0[/tex]
A' = [tex]\frac{d}{dx}(1500x-\frac{3}{2}x^{2})[/tex] = 0
1500 - 3x = 0
3x = 1500
x = 500 ft
From equation (1),
y = 1500 - [tex]\frac{3}{2}\times 500[/tex]
y = 1500 - 750
y = 750 ft
Therefore, for the maximum area of the rectangular plot will be 500 ft × 750 ft.
two fencing 3(500+500) = $3000
other two fencing 2(750+750) = $3000
