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.
What is the fixed cost and net profit per unit produced is?
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To find the fixed cost and net profit per unit produced, we can use the concept of a linear equation.
Let's assume the fixed cost is represented by "FC" and the net profit per unit produced by "NP."
We can set up a system of linear equations based on the given information:
Equation 1: 8,500NP + FC = 47,600 (profit for producing 8,500 units)
Equation 2: 11,500NP + FC = 65,600 (profit for producing 11,500 units)
To solve this system of equations, we'll use the method of substitution.
1. Solve equation 1 for "FC" in terms of "NP":
FC = 47,600 - 8,500NP
2. Substitute this expression for "FC" in equation 2:
11,500NP + (47,600 - 8,500NP) = 65,600
3. Simplify the equation:
11,500NP + 47,600 - 8,500NP = 65,600
11,500NP - 8,500NP = 65,600 - 47,600
3,000NP = 18,000
4. Solve for "NP":
NP = 18,000 / 3,000
NP = 6
Now, we can find the fixed cost by substituting the value of "NP" into equation 1:
FC = 47,600 - 8,500(6)
FC = 47,600 - 51,000
FC = -3,400
Therefore, the fixed cost is -$3,400 (Note: A negative value for fixed cost implies it is an operating loss).
The net profit per unit produced is $6.
So, the fixed cost is -$3,400 (operating loss) and the net profit per unit produced is $6.