Respuesta :
We are given the relationship between the cost in dollars (C) and the number of vacuums (V) to be:
[tex]C\text{ = 24V + 1000}[/tex]From the constraint, we have that the cost(C) must be greater than $49000 and less than $121000
Writing this as inequality:
[tex]\begin{gathered} 24V\text{ + 1000 }\ge\text{ 49000 } \\ 24V\text{ + 1000 }\leq\text{ 121000} \end{gathered}[/tex]Solving the linear inequalities for V:
[tex]\begin{gathered} 24V\text{ + 1000 }\ge\text{ 49000} \\ 24V\text{ }\ge\text{ 49000 - 1000} \\ 24V\text{ }\ge\text{ 48000} \\ \text{Divide both sides by 24} \\ \frac{24V}{24}\text{ }\ge\text{ }\frac{48000}{24} \\ V\text{ }\ge\text{ 2000} \end{gathered}[/tex]Similarly for the second inequality:
[tex]\begin{gathered} 24V\text{ + 1000 }\leq\text{ 121000} \\ 24V\text{ }\leq121000\text{ - 1000} \\ 24V\text{ }\leq\text{ 120000} \\ \text{Divide both sides by 24} \\ \frac{24V}{24}\text{ }\leq\text{ }\frac{120000}{24} \\ V\text{ }\leq5000 \end{gathered}[/tex]Hence, the number of vacuums they can make per week can be between 2000 and 5000 or in inequality:
[tex]2000\text{ }\leq\text{ V }\leq\text{ 5000}[/tex]Answer:
Between 2000 and 5000 vacuums
