Question

A rectangular area of 2,000 square feet is to be fenced on three sides with fence costing $0.30 per foot and on the fourth side with fence costing $0.50 per foot. If x denotes the length of the fourth side and C = ƒ(x ) denotes the corresponding cost of the fence in cents. Give the domain of the function

Answer 1

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 = $\frac{2000}{x}$

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($\frac{2000}{x}$) [Since y = $\frac{2000}{x}$]

f(x) = 0.8x + $\frac{1200}{x}$ 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, ∞).

Answer 2

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