Answer :
To solve the problem of determining which inequality describes the constraints, let's look at each inequality option given in the solution:
1. 1000b - 2500p > 60000: This inequality involves subtracting a term with [tex]\( p \)[/tex] from a term with [tex]\( b \)[/tex], and it suggests that [tex]\( 1000b \)[/tex] must be significantly larger than [tex]\( 2500p \)[/tex] for the result to exceed 60000.
2. 1000b + 2500p > 60000: Here, the addition of [tex]\( 1000b \)[/tex] and [tex]\( 2500p \)[/tex] must together exceed 60000. This could imply a scenario where both [tex]\( b \)[/tex] and [tex]\( p \)[/tex] contribute positively to reaching a value over 60000.
3. 1000b + 2500p \geq 60000: Similar to the second inequality, but with a condition that allows the sum to be equal to 60000, not just greater.
4. 25006 + 1000p \geq 60000: This inequality brings in a specific constant value 25006 added to [tex]\( 1000p \)[/tex], which should reach or exceed 60000. This suggests that the term with [tex]\( p \)[/tex] plays a solo role in balancing out the constant to meet the inequality.
For the constraints described, evaluate what scenario each inequality could represent and how they might compare or relate to real-world applications, such as financial thresholds or resource allocations that need to exceed a certain amount.
Each inequality presents a different combination of the variables and their coefficients or constants, focused on surpassing a given value of 60000, whether strictly greater (>) or allowing equality (≥).
Understanding these distinctions helps justify which inequality best describes the desired conditions you are considering or emphasizing particularly in given scenarios, but all four are valid representations as chosen initially.
1. 1000b - 2500p > 60000: This inequality involves subtracting a term with [tex]\( p \)[/tex] from a term with [tex]\( b \)[/tex], and it suggests that [tex]\( 1000b \)[/tex] must be significantly larger than [tex]\( 2500p \)[/tex] for the result to exceed 60000.
2. 1000b + 2500p > 60000: Here, the addition of [tex]\( 1000b \)[/tex] and [tex]\( 2500p \)[/tex] must together exceed 60000. This could imply a scenario where both [tex]\( b \)[/tex] and [tex]\( p \)[/tex] contribute positively to reaching a value over 60000.
3. 1000b + 2500p \geq 60000: Similar to the second inequality, but with a condition that allows the sum to be equal to 60000, not just greater.
4. 25006 + 1000p \geq 60000: This inequality brings in a specific constant value 25006 added to [tex]\( 1000p \)[/tex], which should reach or exceed 60000. This suggests that the term with [tex]\( p \)[/tex] plays a solo role in balancing out the constant to meet the inequality.
For the constraints described, evaluate what scenario each inequality could represent and how they might compare or relate to real-world applications, such as financial thresholds or resource allocations that need to exceed a certain amount.
Each inequality presents a different combination of the variables and their coefficients or constants, focused on surpassing a given value of 60000, whether strictly greater (>) or allowing equality (≥).
Understanding these distinctions helps justify which inequality best describes the desired conditions you are considering or emphasizing particularly in given scenarios, but all four are valid representations as chosen initially.
