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 + 1,400x
y= 1,800x
The break-even point is the point where cost = revenue
1800x= 48000+1400x
X= 120
The equilibrium quantity is 120 mowers
cost= 4800 + 1400x
x= 120
To find the breakeven point for this plant, you need to determine the number of units at which the cost and revenue equations are equal.
The cost equation is given as:
C(x) = 48,000 + 1,400x
The revenue equation is given as:
R(x) = 1,800x
To find the breakeven point, set the cost equation equal to the revenue equation and solve for x:
48,000 + 1,400x = 1,800x
To solve this equation, isolate the variable terms:
48,000 = 1,800x - 1,400x
Combine like terms:
48,000 = 400x
Divide both sides by 400:
x = 48,000 / 400
x = 120
Therefore, the breakeven point occurs when the plant produces and sells 120 riding lawn mowers.