A small plant manufactures riding lawn mowers. The plant has fixed cost (leases, insurance, etc.) of $48,000 per day and variable cost (labor, materials, etc.) of $1,400 per unit produced. The mowers are sold for $1,800 each. So the cost and revenue equations are
y= 48,000 + 1,800x
y= 1,800x
no,
cost = 4800 + 1400x
To find the breakeven point, you need to set the cost equation equal to the revenue equation and solve for x.
The cost equation is:
y = 48,000 + 1,400x
The revenue equation is:
y = 1,800x
Setting these two equations equal to each other, we get:
48,000 + 1,400x = 1,800x
Now, we can solve for x by isolating the variable on one side of the equation:
1,400x - 1,800x = 48,000
-400x = 48,000
x = 48,000 / -400
x = -120
Since you can't have negative units, we can conclude that there is no breakeven point in this scenario.
Explanation of the process:
1. Start with the cost equation, which includes both fixed costs (48,000) and variable costs (1,400x, where x is the number of units produced).
2. Set up the revenue equation, which is simply the selling price (1,800) multiplied by the number of units produced (x).
3. Set the cost equation equal to the revenue equation, since the breakeven point occurs when the costs and revenue are equal.
4. Simplify the equation by combining like terms and isolating the variable x.
5. Solve for x by performing the necessary arithmetic operations.
6. Interpret the results - in this case, we find that the breakeven point cannot be achieved because the number of units produced would be negative.