specifications are not the same. $($b$)$ The company wants to minimize total cost. Give the objective function.

Min

$($c$)$ Give the constraints for the problem.

machine $1$ production capacity

machine $2$ production capacity

machine $3$ production capacity

machine $4$ production capacity

demand

$($d$)$ Write a constraint to ensure that if machine $3$ is used, machine $2$ cannot be$.$

$($a$)$ This problem requires two different kinds of decision variables. Clearly define each kind. $($Select all that apply.$)$

$C_i=$ the maximum capacity for hoses produced on machine $i$

$F_i=1$ if the variable cost of producing hoses on machine i exceeds the fixed cost; $0$ otherwise

$P_i=$ number of hoses produced on machine $i$

$D_i=$ the minimum demand for hoses produced on machine $i$

$U_i=1$ if machine $i$ is used; $0$ otherwise