Answer:
$3
Step-by-step explanation:
Given that:
p = 8 - ln(x) when 5 < x < 500
where;
x = The total number of dogs sold
Then;
The total revenue = x * p
R = x(8 - ln(x))
R = 8x - xln(x)
The Company thus pays 1 dollar per dog
i.e.
The total cost C = 1 * x = x
Then: Profit = R - C
P = 8x - xln(x) - x
P = 7x - xln(x)
Differentiating P in respect to x
dP/dx = 7 - d/dx(xln(x))
dP/dx = 7 - x*d/dx(ln(x)) - ln(x)*d/dx(x)
dP/dx = 7 - x(1/x) - ln(x)
dP/dx = 6 - ln(x)
Since this must be maximized, dP/dx is set to be equal to 0
6 - ln(x) = 0
ln(x) = 6
x = e^6
Now, p = 8 - ln(x)
Plug in the value of x :
p = 8 - ln(e^5)
p = 8 - 5
p = 3
Therefore, each dog must be priced at $3 to maximize the profit.
Answer:
x = 1/2
and
y = -1
Step-by-step explanation:
8x + 3y = 1
4x + 2y = 0
Multiply 4x + 2y = 0 by 2
8x + 3y = 1
8x + 4y = 0
8x + 4y = 0 minus 8x + 3y = 1
y = -1
For 8x + 3y = 1 plug in y = -1
8x + 3(-1) = 1
8x - 3 x 1 = 1
8x - 3 = 1
Add 3 to both sides
8x - 3 + 3 = 1 + 3
8x = 4
Divide both sides by 8
8x/8 (cancels out) = 4/8
x = 1/2
Answer:
x ≓ 3.242593855
Step-by-step explanation:
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of slides ridden and y represent the total cost. Hence:
1) For option 1, the table is shown. It passes through (2,10) and (6, 20). The equation is:
2) For option 2, the equation is given by y = 5x + 7.5
3) For option 3, the graph passes through (30, 100) and (10, 40). Hence the equation is:
Option 2 has the highest rate
Answer:
Step-by-step explanation:
refer to photo