Aberdeen Computer Corporation $($ACC$)$ is located in Aberdeen, Washington. The company has developed Jeeves, a voice$-$activated Internet assistant for the home. This product is manufactured at four plants, located in Atlanta, Kansas City, Aberdeen, and Austin. After production, the units are shipped to three warehouses located in Nashville, San Jose, and Houston. ACC sells through the retail channel. In particular, five different retailers currently sell Jeeves$$Sears$,$ Best Buy, Staples, Walmart, and Office Depot. ACC makes weekly shipments to the main warehouses of these five retailers.

The shipping cost from each plant to each warehouse, along with the production cost and weekly production capacity at each plant, are given in the table below.

Plant Shipping Cost $($$$/$unit$)$ Production Cost $($$ $/$unit$)$ Capacity $($units$/$week$)$

Nashville San Jose Houston

Atlanta $ $30$ $ $40$ $ $50$ $ $208100$

Kansas City $ $25$ $ $45$ $ $40$ $ $214400$

Aberdeen $ $45$ $ $30$ $ $55$ $ $215400$

Austin $ $30$ $ $50$ $ $30$ $ $210300$

The shipping cost from each warehouse to each customer, the variable cost $($cost per unit moved through the warehouse$),$ the capacity $($maximum number of units that can be moved through the warehouse per week$)$ for each warehouse, and the weekly demand for each customer are given in the table below.

Warehouse Shipping Cost $($$$/$Unit$)$ Variable Cost $($$ $/$unit$)$ Capacity $($units$/$week$)$

Sears Best Buy Staples Walmart Office Depot

Nashville $ $40$ $ $45$ $ $30$ $ $25$ $ $20$ $ $4300$

San Jose $ $15$ $ $50$ $ $25$ $ $15$ $ $40$ $ $5500$

Houston $ $50$ $ $35$ $ $15$ $ $40$ $ $50$ $ $5500$

Customer demand $($per week$)1005075300150$

Click here for the Excel Data File

Formulate and solve a linear programming model in a spreadsheet.

Determine the plan for weekly production and distribution of Jeeves from the various plants, through the warehouses, to the customers that will minimize total costs.

Note: Leave no cells blank. Enter $"0"$ wherever required.

Determine the total cost.