Answer:
95 rooms
Explanation:
R = 3log(n^2 + 10n)
R = 12
3log(n^2 + 10n) = 12
Divide both sides by 3
Log(n^2 + 10n) = 4
Take log off both sides
n^2 + 10n = 10^4
n^2 + 10n - 10000 = 0
Solve the equation above using the quadratic formula
n = [-b + or - √(b^2 - 4ac)] ÷ 2a
The value of n must be positive
Therefore, n = [-b + √(b^2 - 4ac)] ÷ 2a
a = 1, b = 10, c = -10000
n = [-10 + √(10^2 - 4(1)(-10000)] ÷ 2(1) = (-10 + √40100) ÷ 2 = (-10 +200.25) ÷ 2 = 190.25 ÷ 2 = 95.125
Therefore, minimum number of rooms that must be occupied daily for the hotel to be profitable is 95