I'm really confused about the wording. y-2/5? <em>time </em>y-2/5?
Let the number of men and women in the room be represented by an arbitrary constant, x and y respectively.
x + y = 96
y = 96 - x
When one man leaves, we get: x - 1
When one woman replaces the man, we get: y + 1
So, y + 1 = 3(x - 1)
Substituting y = 96 - x, we get:
96 - x + 1 = 3x - 3
97 + 3 = 4x
100 = 4x
x = 25
Thus, there were 25 men and 41 women in the room originally.
You can estimate the length of a book by its thickness and how small the words are.
A.) Revenue = price * quantity = px = -1/20x^2 + 1060x
R(x) = -1/20x^2 + 1060x.
b.) Profit = Revenue - Cost = R(x) - C(x) = -1/20x^2 + 1060x - 120x - 5000
P(x) = -1/20x^2 + 940x - 5000
c.) For maximum profit, dP/dx = 0
-1/10x + 940 = 0
1/10x = 940
x = 940 * 10 = 9,400
x = 9,400
Maximum profit = P(9400) = -1/20(9400)^2 + 940(9400) - 5000 = $4,413,000
d.) The price to be charged for maximum profit = -1/20(9400) + 1060 = $590