Answer :
To solve this problem, we need to select the inequality that best represents the constraints of the situation described. We have the following options:
1. [tex]\( 1250t + 2c > 20000 \)[/tex]
2. [tex]\( 2t - 1250c < 20000 \)[/tex]
3. [tex]\( 2t - 1250c > 20000 \)[/tex]
4. [tex]\( 1250t - 2c > 20000 \)[/tex]
### Step-by-Step Analysis:
1. Identify the Variables:
- [tex]\( t \)[/tex] and [tex]\( c \)[/tex] are the variables. They could represent different quantities, like time, cost, or other operational metrics.
2. Understand the Context:
- Notice the similar structure in the inequalities: Some inequalities emphasize the coefficient of 1250 with [tex]\( t \)[/tex], while others focus on 2 with either [tex]\( c \)[/tex] or [tex]\( t \)[/tex].
3. Review Each Option:
- Option 1: [tex]\( 1250t + 2c > 20000 \)[/tex]
- This suggests that a combination of factors [tex]\( t \)[/tex] (multiplied by a large factor 1250) and [tex]\( c \)[/tex] adds up to exceed 20000.
- Option 2 and 3: [tex]\( 2t - 1250c < 20000 \)[/tex] and [tex]\( 2t - 1250c > 20000 \)[/tex]
- These show that there’s a negative impact (-1250) involving [tex]\( c \)[/tex] and 2 multiplied by [tex]\( t \)[/tex], either exceeding or not reaching 20000.
- Option 4: [tex]\( 1250t - 2c > 20000 \)[/tex]
- This indicates a strong influence of [tex]\( t \)[/tex] versus a smaller factor with [tex]\( c \)[/tex] contributing to the sum to exceed 20000.
4. Choose the Appropriate Constraint:
- Since the task is to find a constraint, often representative factors (like significant costs or resource allocations) play a pivotal role in driving the inequality. In this context, we look for a large impact provided by the value multiplied by 1250.
The inequality that logically represents this combination, where a large impact is necessary to exceed a threshold value of 20000, is:
[tex]\[ 1250t + 2c > 20000 \][/tex]
Thus, the chosen inequality is:
[tex]\[ 1250t + 2c > 20000 \][/tex]
This condition effectively captures the interaction and impact of the variables ensuring constraints are met or exceeded.
1. [tex]\( 1250t + 2c > 20000 \)[/tex]
2. [tex]\( 2t - 1250c < 20000 \)[/tex]
3. [tex]\( 2t - 1250c > 20000 \)[/tex]
4. [tex]\( 1250t - 2c > 20000 \)[/tex]
### Step-by-Step Analysis:
1. Identify the Variables:
- [tex]\( t \)[/tex] and [tex]\( c \)[/tex] are the variables. They could represent different quantities, like time, cost, or other operational metrics.
2. Understand the Context:
- Notice the similar structure in the inequalities: Some inequalities emphasize the coefficient of 1250 with [tex]\( t \)[/tex], while others focus on 2 with either [tex]\( c \)[/tex] or [tex]\( t \)[/tex].
3. Review Each Option:
- Option 1: [tex]\( 1250t + 2c > 20000 \)[/tex]
- This suggests that a combination of factors [tex]\( t \)[/tex] (multiplied by a large factor 1250) and [tex]\( c \)[/tex] adds up to exceed 20000.
- Option 2 and 3: [tex]\( 2t - 1250c < 20000 \)[/tex] and [tex]\( 2t - 1250c > 20000 \)[/tex]
- These show that there’s a negative impact (-1250) involving [tex]\( c \)[/tex] and 2 multiplied by [tex]\( t \)[/tex], either exceeding or not reaching 20000.
- Option 4: [tex]\( 1250t - 2c > 20000 \)[/tex]
- This indicates a strong influence of [tex]\( t \)[/tex] versus a smaller factor with [tex]\( c \)[/tex] contributing to the sum to exceed 20000.
4. Choose the Appropriate Constraint:
- Since the task is to find a constraint, often representative factors (like significant costs or resource allocations) play a pivotal role in driving the inequality. In this context, we look for a large impact provided by the value multiplied by 1250.
The inequality that logically represents this combination, where a large impact is necessary to exceed a threshold value of 20000, is:
[tex]\[ 1250t + 2c > 20000 \][/tex]
Thus, the chosen inequality is:
[tex]\[ 1250t + 2c > 20000 \][/tex]
This condition effectively captures the interaction and impact of the variables ensuring constraints are met or exceeded.
