Let's solve the problem step-by-step using the given data and the assumptions made by the sales manager:
### Step 1: Define the initial values:
1. Current Sales Units: [tex]\(1000\)[/tex] units
2. Selling Price per Unit: [tex]\(\$50\)[/tex]
3. Monthly Advertising Budget: [tex]\(\$10,000\)[/tex]
4. Fixed Costs: [tex]\(\$20,000\)[/tex]
5. Variable Costs per Unit: [tex]\(\$20\)[/tex]
### Step 2: Calculate current operating income:
1. Current Revenue:
[tex]\[ \text{Current Revenue} = \text{Current Sales Units} \times \text{Selling Price per Unit} = 1000 \times 50 = \$50,000 \][/tex]
2. Current Variable Costs:
[tex]\[ \text{Current Variable Costs} = \text{Current Sales Units} \times \text{Variable Costs per Unit} = 1000 \times 20 = \$20,000 \][/tex]
3. Current Operating Income:
[tex]\[ \text{Current Operating Income} = \text{Current Revenue} - \text{Current Variable Costs} - \text{Fixed Costs} - \text{Monthly Advertising Budget} \][/tex]
[tex]\[ \text{Current Operating Income} = 50,000 - 20,000 - 20,000 - 10,000 = \$0 \][/tex]
### Step 3: Calculate the new values based on the manager's assumptions:
1. New Selling Price (10% reduction):
[tex]\[ \text{New Selling Price} = \text{Selling Price per Unit} \times (1 - 0.10) = 50 \times 0.90 = \$45 \][/tex]
2. New Advertising Budget (increase by \[tex]$39,000):
\[ \text{New Advertising Budget} = \text{Monthly Advertising Budget} + 39,000 = 10,000 + 39,000 = \$[/tex]49,000 \]
3. New Sales Units (doubling sales):
[tex]\[ \text{New Sales Units} = \text{Current Sales Units} \times 2 = 1000 \times 2 = 2000 \][/tex]
### Step 4: Calculate the new financial values:
1. New Revenue:
[tex]\[ \text{New Revenue} = \text{New Sales Units} \times \text{New Selling Price} = 2000 \times 45 = \$90,000 \][/tex]
2. New Variable Costs:
[tex]\[ \text{New Variable Costs} = \text{New Sales Units} \times \text{Variable Costs per Unit} = 2000 \times 20 = \$40,000 \][/tex]
3. New Operating Income:
[tex]\[ \text{New Operating Income} = \text{New Revenue} - \text{New Variable Costs} - \text{Fixed Costs} - \text{New Advertising Budget} \][/tex]
[tex]\[ \text{New Operating Income} = 90,000 - 40,000 - 20,000 - 49,000 = -\$19,000 \][/tex]
### Summary:
- The current operating income is [tex]\( \$0 \)[/tex].
- The new operating income, after applying the manager's strategies, would be a loss of [tex]\( -\$19,000 \)[/tex].
Thus, if the sales manager's assumptions are correct, the revised net operating income would be a loss of \$19,000.
