Set up fee is $40.00 per person it is $800.00 rental per month. How many flights must be sold to maximize profit? show work algebraically
To determine the number of flights that must be sold to maximize profit, we first need to understand the profit equation.
Let's define:
x = number of flights sold
The total revenue can be calculated by multiplying the number of flights sold by the rental fee per month:
Revenue = x * $800.00
The total cost can be calculated by multiplying the number of flights sold by the set-up fee per person:
Cost = x * $40.00
The profit equation is calculated by subtracting the cost from the revenue:
Profit = Revenue - Cost
Now, let's substitute the expressions for revenue and cost into the profit equation:
Profit = (x * $800.00) - (x * $40.00)
Simplifying the equation:
Profit = $800.00x - $40.00x
Profit = $760.00x
To maximize profit, we need to find the maximum point of the profit equation. This occurs when the slope is zero. In our case, the slope can be found by taking the derivative of the profit equation with respect to x:
d(Profit)/dx = d($760.00x)/dx
= $760.00
Setting the derivative equal to zero:
$760.00 = 0
Since the slope is constant and positive, it does not equal zero. Hence, there is no maximum point. This implies that as the number of flights sold increases, the profit will continue to increase.
Therefore, there is no specific number of flights to sell to maximize profit. The profit will continue to increase as more flights are sold.