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Check My Work $(2$ remaining$)$

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.

Plant Store A Store B Store C Capacity

$1$ $$4\mathrm{.}50$ $$3\mathrm{.}10$ $$2\mathrm{.}00280$

$2$ $$5\mathrm{.}10$ $$2\mathrm{.}60$ $$3\mathrm{.}80460$

$3$ $$4\mathrm{.}10$ $$2\mathrm{.}90$ $$4\mathrm{.}00300$

Demand $250600150$

Formulate a linear optimization model for this problem, implement your model on a spreadsheet, 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 Store 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

Min

X$11+$

X$12+$

X$13+$

X$21+$

X$22+$

X$23+$

X$31+$

X$32+$

X$33$

Subject to the constraints

X$11+$

X$12+$

X$13$

$-$Select$-$

X$21+$

X$22+$

X$23$

$-$Select$-$

X$31+$

X$32+$

X$33$

$-$Select$-$

X$11+$

X$21+$

X$31$

$-$Select$-$

X$12+$

X$22+$

X$32$

$-$Select$-$

X$13+$

X$23+$

X$33$

$-$Select$-$

X$11,$ X$12,$ X$13,$ X$21,$ X$22,$ X$23,$ X$31,$ X$32,$ X$33>=0$

What is the value of total distribution costs at the optimal solution? Use the Excel solver to find the optimal solution. Round your answer to the nearest dollar.

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