To address the given questions, let's break down the provided information and analyze it step by step.
### Step 1: Calculate the Profit per Pound of Selling T-Bone Steak as Initially Cut
The initial profit for selling a 1-pound (16-ounce) T-bone steak, as initially cut, is calculated as follows:
- Selling Price per Pound: \[tex]$7.95
- Joint Costs: \$[/tex]3.80
- Profit per Pound Initially Cut:
[tex]\[
\text{Profit per pound} = \text{Selling Price per Pound} - \text{Joint Costs} = \$7.95 - \$3.80 = \$4.15
\][/tex]
### Step 2: Calculate the Total Profit from Further Processing into Filet Mignon and New York Cut
When a 1-pound T-bone steak is further processed:
- It yields 6 ounces of filet mignon and 8 ounces of New York cut.
- Further Processing Cost: \[tex]$0.55
First, we convert the weights from ounces to pounds:
- Filet Mignon Weight:
\[
6 \text{ ounces} = \frac{6}{16} \text{ pounds} = 0.375 \text{ pounds}
\]
- New York Cut Weight:
\[
8 \text{ ounces} = \frac{8}{16} \text{ pounds} = 0.5 \text{ pounds}
\]
Next, we calculate the selling price for each cut:
- Filet Mignon Selling Price:
\[
\text{Selling Price of Filet Mignon} = 0.375 \text{ pounds} \times \$[/tex]12.00 \text{ per pound} = \[tex]$4.50
\]
- New York Cut Selling Price:
\[
\text{Selling Price of New York Cut} = 0.5 \text{ pounds} \times \$[/tex]8.80 \text{ per pound} = \[tex]$4.40
\]
The total profit after further processing (taking into account the additional processing cost) is:
- Total Revenue from Further Processing:
\[
\text{Total Revenue} = \$[/tex]4.50 \text{ (filet mignon)} + \[tex]$4.40 \text{ (New York cut)} = \$[/tex]8.90
\]
- Total Cost of Further Processing:
[tex]\[
\text{Further Processing Cost} = \$0.55
\][/tex]
- Total Profit from Further Processing:
[tex]\[
\text{Total Profit Processed} = \text{Total Revenue} - \text{Further Processing Cost} = \$8.90 - \$0.55 = \$8.35
\][/tex]
### Step 3: Determine the Financial Advantage or Disadvantage
To determine the financial advantage or disadvantage, we need to compare the profit from the two methods:
- Profit per pound initially cut: \[tex]$4.15
- Total profit from further processing: \$[/tex]8.35
- Financial Advantage (Disadvantage):
[tex]\[
\text{Advantage (Disadvantage)} = \text{Total Profit Processed} - \text{Profit per Pound Initially Cut} = \$8.35 - \$4.15 = \$4.20
\][/tex]
### Step 4: Make a Recommendation
Since the financial advantage of further processing one T-bone steak into filet mignon and New York cut steaks is \[tex]$4.20, we recommend that Lone Star Meat Packers should process further the T-bone steaks rather than selling them as initially cut.
### Conclusion:
1. Financial Advantage (Disadvantage) of Further Processing: The financial advantage of further processing one T-bone steak into filet mignon and New York cut steaks is \$[/tex]4.20.
2. Recommendation: It is recommended to process further the T-bone steaks into filet mignon and New York cut steaks.
