Each unit sells: $80
Each unit costs to make: $32
Fixed costs: 72,000
Goal: 2,000 units sold
If they meet their goal, let's see how that would go:
(2,000 * 80) - (2,000 * 32) - 72,000 = ?
160,000 - 64,000 - 72,000 = 24,000
24,000 is the profit they would make for hitting their goal.
Question 1:
What is the break-even point? The break-even means they make no money, but they also lose no money. So that final number (24,000) would be 0 instead. How many units would they have to make to hit zero?
(x * 80) - (x * 32) - 72,000 = 0.
80x - 32x = 72,000
48x = 72,000
x = 1500 units
We can verify by using our first formula we've already determined, using this new value for units.
(1,500* 80) - (1,500 * 32) - 72,000 = ?
120,000 - 48,000 - 72,000 = 0? True!
Question 2: If they increase their expenses by 16,000, what is their new break even point?
(x * 80) - (x * 32) - 72,000 - 16000 = 0.
80x - 32x - 88000 = 0
48x = 88000
x = 1833
Question 3: 10% reduction in selling price and 10% increase in sales. (Assuming based off the original formula the problem provided.)
Original: (2,000 * 80) - (2,000 * 32) - 72,000 = ?
10% Reduction in price: 8
80-8 = 72
10% increase in sales: 200
2000 + 200 = 2200
Plugin to our formula:
(2200 * 72) - (2200 * 32) - 72,000 = ?
158400 - 70400 - 72,000 = 16,000
Since this number is positive, this is income. (D)
