Answer :
Let's denote the investment amounts in stocks A, B, and C as [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(16,000 - x - y\)[/tex] respectively since the total amount to be invested is \[tex]$16,000.
We need to state the constraints based on the given conditions:
1. Minimum investment in each stock:
- Stock A: \(x\)
- Stock B: \(y\)
- Stock C: \(16,000 - x - y\)
Since at least \$[/tex]1,000 must be invested in each stock:
[tex]\[ x \geq 1000 \][/tex]
[tex]\[ y \geq 1000 \][/tex]
[tex]\[ 16000 - x - y \geq 1000 \][/tex]
2. Maximum investment in stock C:
[tex]\[ 16000 - x - y \leq 7000 \][/tex]
3. Limiting stock C to less than 4 times stock A:
[tex]\[ 16000 - x - y \leq 4x \][/tex]
4. Investment in stock B less than twice as much as in stock A:
[tex]\[ y \leq 2x \][/tex]
Now, let's state the constraints clearly:
- Stock A: [tex]\(x \geq 1000\)[/tex]
- Stock B: [tex]\(y \geq 1000\)[/tex] and [tex]\(y \leq 2x\)[/tex]
- Stock C: [tex]\[16000 - x - y \geq 1000\][/tex]
[tex]\[ 16000 - x - y \leq 7000 \][/tex]
[tex]\[ 16000 - x - y \leq 4x \][/tex]
Thus, the complete constraints are:
- Stock A: [tex]\(x \geq 1000\)[/tex]
- Stock B: [tex]\(y \geq 1000\)[/tex] and [tex]\(y \leq 2x\)[/tex]
- Stock C: [tex]\[16000 - x - y \geq 1000\][/tex]
[tex]\[ 16000 - x - y \leq 7000 \][/tex]
[tex]\[ 16000 - x - y \leq 4x \][/tex]
[tex]\[ x \geq 1000 \][/tex]
[tex]\[ y \geq 1000 \][/tex]
[tex]\[ 16000 - x - y \geq 1000 \][/tex]
2. Maximum investment in stock C:
[tex]\[ 16000 - x - y \leq 7000 \][/tex]
3. Limiting stock C to less than 4 times stock A:
[tex]\[ 16000 - x - y \leq 4x \][/tex]
4. Investment in stock B less than twice as much as in stock A:
[tex]\[ y \leq 2x \][/tex]
Now, let's state the constraints clearly:
- Stock A: [tex]\(x \geq 1000\)[/tex]
- Stock B: [tex]\(y \geq 1000\)[/tex] and [tex]\(y \leq 2x\)[/tex]
- Stock C: [tex]\[16000 - x - y \geq 1000\][/tex]
[tex]\[ 16000 - x - y \leq 7000 \][/tex]
[tex]\[ 16000 - x - y \leq 4x \][/tex]
Thus, the complete constraints are:
- Stock A: [tex]\(x \geq 1000\)[/tex]
- Stock B: [tex]\(y \geq 1000\)[/tex] and [tex]\(y \leq 2x\)[/tex]
- Stock C: [tex]\[16000 - x - y \geq 1000\][/tex]
[tex]\[ 16000 - x - y \leq 7000 \][/tex]
[tex]\[ 16000 - x - y \leq 4x \][/tex]