Each high school has a capacity of $1,000$ students.

You have been asked to develop a linear programming model so as to minimize the total number of student miles traveled Decision variable $x_{ij}$ : Number of students living in sector i traveling to school located in sector $j.$ The number of decision variables for the model $=15.$

a$)$ The objective function, for the LP model $=$

Minimize $Z=5x_{AB}+8x_{AC}+6x_{AE}+$

$0x_{BB}+4x_{BC}+12x_{BE}+$

$4x_{CB}+0x_{CC}+7x_{CE}+$

$7x_{DB}+2x_{DC}+5x_{DE}+$

$12x_{EB}+7x_{EC}+0x_{EE}$

Subject to:

$x_{AB}+x_{AC}+x_{AE}=750$ number $of$ students $in$ sector $A$

$x_{BB}+x_{BC}+x_{BE}=600$ number $of$ students $in$ sector $B$

$x_{CB}+x_{CC}+x_{CE}=150$ number $of$ students $in$ sector $C$

$x_{DB}+x_{DC}+x_{DE}=800$ number $of$ students $in$ sector $D$

$x_{EB}+x_{EC}+x_{EE}=500$ number $of$ students $in$ sector $E$

$x_{AB}+x_{BB}+x_{CB}+x_{DB}+x_{EB}1,000$ school $B$ capacity

$x_{AC}+x_{BC}+x_{CC}+x_{DC}+x_{EC}1,000$ school $C$ capacity

$x_{AE}+x_{BE}+x_{CE}+x_{DE}+x_{EE}1,000$ school $E$ capacity

For all $x_{ij}0$ non negativity condition

non negativity condition

b$)$ Using a computer software for solving LP$,$ the objective value at the optimal solution achieved is: Minimum number of total miles traveled $($objective value$)=($round your response to a whole number$).$