A manufacturer can produce 8,500 units for a total profit of 47,600.00 dollars, but if he increases his production to 11,500 units, then his profit becomes $65,600.00.
It follows that his fixed cost is? and his net profit per unit produced is?
Treat your information as 2 ordered pairs of the form
(x,p) where x is the number of units, and p is the profit.
So you have (8500, 47600) and (11500, 65600)
slope = (65600-47600)/(11500-8500) = 6
so your equation in the form y = mx + b is
p = 6x + b
sub in the first point
47600 = 6(8500) + b
b = -3400
p = 6x - 3400
Can you interpret this equation?
e.g. What is his "profit" if he makes zero units ?
I got that far. But I still do not know how to find the fixed cost and net profit from the p(x) equation.
To find the fixed cost and net profit per unit produced, we can use the information provided.
Let's start by calculating the variable cost per unit produced:
Variable cost per unit = (Total Profit at higher production - Total Profit at lower production) / (Number of units at higher production - Number of units at lower production)
Variable cost per unit = ($65,600.00 - $47,600.00) / (11,500 - 8,500)
Variable cost per unit = $18,000.00 / 3,000
Variable cost per unit = $6.00
Now, we can calculate the fixed cost by subtracting the variable cost per unit from the total cost at the lower production level:
Fixed cost = Total profit at lower production - (Variable cost per unit x Number of units at lower production)
Fixed cost = $47,600.00 - ($6.00 x 8,500)
Fixed cost = $47,600.00 - $51,000.00
Fixed cost = -$3,400.00
The result is negative, indicating that there might be an error in the provided data or calculations. The fixed cost cannot be negative, so it's important to double-check the information and calculations.