Respuesta :
2000 = x * y
y = 2000 / x
c = 0.3 * (2y + x) + 0.5x = 0.6y + 0.8x = 0.6 * 2000 / x + 0.8x = 1200/x + 0.8x
y = 2000 / x
c = 0.3 * (2y + x) + 0.5x = 0.6y + 0.8x = 0.6 * 2000 / x + 0.8x = 1200/x + 0.8x
Answer:
Domain of the function will be (0, ∞).
Step-by-step explanation:
A rectangular area is to be fenced on three sides with fence costing $0.30 and 4th side with the fence costing $0.50 per foot.
Let the length and width of the rectangle is x foot and y foot.
Therefore, area of the rectangular area = xy square feet.
xy = 2000
y = [tex]\frac{2000}{x}[/tex]
Now cost of fencing 3 sides = (0.3)(x+2y) and cost of fencing the fourth side = 0.50x
Total cost of the fencing C = 0.3(x + 2y) + 0.5x
C = 0.3x + 0.6y + 0.5x
C = 0.8x + 0.6y
C = 0.8x + 0.6([tex]\frac{2000}{x}[/tex]) [Since y = [tex]\frac{2000}{x}[/tex]]
f(x) = 0.8x + [tex]\frac{1200}{x}[/tex] is the function
Since this function is not defined at x = 0
Domain of the function must be (-∞, 0) ∪ (0, ∞) but length of the fence can't be in the interval (-∞, 0).
Therefore, domain will be (0, ∞).
