Milford Lumber Company ships construction materials from three wood$-$processing plants to three retail stores. The shipping cost, monthly production capacities, and monthly demand for framing lumber are given below.

$\backslash$table$[[$Plant$,$Store $A,$Store B$,$Store C$,$Capacity$],[1,$$$5\mathrm{.}50,$$$3\mathrm{.}30,$$$1\mathrm{.}20,280],[2,$$$5\mathrm{.}80,$$$2\mathrm{.}40,$$$2\mathrm{.}50,480],[3,$$$2\mathrm{.}90,$$$1\mathrm{.}70,$$$4\mathrm{.}60,450],[$Demand$,300,530,350,]]$

Formulate a linear optimization model for this problem, implement your model on a spredsheet, and use Excel Solver to find a solution that minimizes total distribution costs. If the constant is equal to one, enter $"1".$

Let:

$x_{11}=$ number of components produced in Plant $1$ and supplied to Store A

$x_{12}=$ number of components produced in Plant $1$ and supplied to ${?}^{C}B$

$x_{13}=$ number of components produced in Plant $1$ and supplied to Store $C$

$x_{21}=$ number of components produced in Plant $2$ and supplied to Store A

$x_{22}=$ number of components produced in Plant $2$ and supplied to Store B

$x_{23}=$ number of components produced in Plant $2$ and supplied to Store $C$

$x_{31}=$ number of components produced in Plant $3$ and supplied to Store A

$x_{32}=$ number of components produced in Plant $3$ and supplied to Store $B$

$x_{33}=$ number of components produced in Plant $3$ and supplied to Store $C$