(Related to Checkpoint​ 4.1) ​(Analyzing liquidity) Apex Fabricating​, ​Inc., manufactures fenders and other​ after-market body panels for older automobiles. At the close of last​ year, the firm had ​$11 comma 209 comma 536 in current assets and ​$4 comma 151 comma 680 in current liabilities. The​ company's managers want to increase the​ firm's inventory, which will be financed using​ short-term debt. How much can the firm increase its inventory without its current ratio falling below 2.1 ​(assuming all other current assets and current liabilities remain​ constant)?

To determine how much Apex Fabricating, Inc. can increase its inventory without the current ratio falling below 2.1, we need to use the formula for the **current ratio**:

\[
\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}}
\]

### Step 1: Determine the current situation
- **Current assets (CA)** = $11,209,536
- **Current liabilities (CL)** = $4,151,680

The current ratio is:

\[
\text{Current Ratio} = \frac{11,209,536}{4,151,680} \approx 2.7
\]

### Step 2: New current ratio formula
Let $ x $ represent the increase in inventory, which is added to current assets and current liabilities (since it is financed by short-term debt). The new current assets will be $ 11,209,536 + x $, and the new current liabilities will be $ 4,151,680 + x $. 

The current ratio should not fall below 2.1:

\[
\frac{11,209,536 + x}{4,151,680 + x} = 2.1
\]

### Step 3: Solve for $ x $
Now, solve this equation for $ x $:

\[
11,209,536 + x = 2.1(4,151,680 + x)
\]

Expand the right side:

\[
11,209,536 + x = 8,718,528 + 2.1x
\]

Simplify:

\[
11,209,536 - 8,718,528 = 2.1x - x
\]

\[
2,491,008 = 1.1x
\]

Now, solve for $ x $:

\[
x = \frac{2,491,008}{1.1} \approx 2,264,553
\]

### Step 4: Conclusion
Apex Fabricating, Inc. can increase its inventory by approximately **$2,264,553** without the current ratio falling below 2.1.

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Do you want more details, or do you have any questions?

Here are 5 related questions:
1. How is the current ratio used to assess a company's liquidity?
2. What risks are associated with increasing inventory through short-term debt?
3. Why is it important for Apex Fabricating to maintain a current ratio above a certain level?
4. How would changes in other current assets or liabilities affect this calculation?
5. What other liquidity ratios should Apex Fabricating monitor?

**Tip**: Monitoring the current ratio over time helps businesses ensure they have enough short-term assets to cover short-term liabilities.

Apex Fabricating​, ​Inc., manufactures fenders and other​ after-market body panels for older automobiles. At the close of last​ year, the firm had $11,209,536 in current assets and $4,151,680 in current liabilities. The​ company's managers want to increase the​ firm's inventory, which will be financed using​ short-term debt. How much can the firm increase its inventory without its current ratio falling below 2.1 ​(assuming all other current assets and current liabilities remain​ constant)?

Solve a real-world business problem involving Apex Fabricating, Inc. Learn how to calculate how much inventory the company can increase, using algebra and the current ratio formula. Suitable for students or professionals interested in financial mathematics. Initial values: $11,209,536 in current assets and $4,151,680 in current liabilities.

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