How many units of the product were sold during the most recent year? (to nearest unit)

Steps to Solve

1. Identify the variables
   We have the following variables:

• Total fixed costs ( = 14,000 )
• Variable costs per unit ( = 35 )
• Selling price per unit ( = 54 )
• Loss ( = 2,000 )

2. Determine total costs
   Total costs can be computed as the sum of total fixed costs and total variable costs. The variable costs will be calculated based on the number of units sold ( x ):
   Total costs ( = \text{Total fixed costs} + (\text{Variable costs per unit} \times x) )
   Also, we know that Loss ( = \text{Total Revenue} - \text{Total Costs} ), where Total Revenue is given by:
   Total Revenue ( = \text{Selling price per unit} \times x )
   Thus, we set up the equation for loss:
   $$ 2,000 = (54 \times x) - \left(14,000 + (35 \times x)\right) $$

3. Rearrange the equation
   Expanding and rearranging gives us:
   $$ 2,000 = 54x - 14,000 - 35x $$
   Combine like terms:
   $$ 2,000 = 19x - 14,000 $$

4. Isolate ( x )
   Adding ( 14,000 ) to both sides:
   $$ 16,000 = 19x $$
   Now, dividing by ( 19 ) gives:
   $$ x = \frac{16,000}{19} \approx 842.11 $$

5. Round to the nearest unit
   Since the question asks for units sold to the nearest unit, we round ( 842.11 ) to ( 842 ).