Develop a linear programming model to minimize cost. $($Let $x_{ij}$ be the number of square yards of carpet which flows from node $i$ to node $j.)$

Min

s$.$t$.$

Beginning Inventory Flow

Quarter $1$ Production Flow

Quarter $2$ Production Flow

Quarter $3$ Production Flow

Quarter $4$ Production Flow

Quarter $1$ Demand Flow

Quarter $2$ Demand Flow

Quarter $3$ Demand Flow

Quarter $4$ Demand Flow

Ending Inventory Flow

$x_{ij}0$ for all $i,j.$

Solve the linear program to find the optimal solution $($in dollars$).$

$(x_{16},x_{26},x_{37},x_{48},x_{59},x_{67},x_{78},x_{89},x_{910})=$ with cost $