$7\mathrm{.}19.$ Aberdeen Computer Corp. $($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 Aus$-$

tin. 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, Fry$\text{'}$s$,$ Walmart, and Office Depot.

ACC makes weekly shipments to the main warehouses of these

five retailers. The shipping cost from each plant to each ware$-$

house, along with the production cost and weekly production

capacity at each plant, are given in the table below.

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.

a$.$ Formulate and solve a linear programming model

in a spreadsheet to determine the plan for weekly

production and distribution of Jeeves from the vari$-$

ous plants, through the warehouses, to the custom$-$

ers that will minimize total costs.

b$.$ Now suppose that ACC is considering saving money

by closing some of its production facilities and$/$or

warehouses. Suppose there is a fixed cost to operate

each plant and each warehouse as indicated in the

following tables. Add binary variables to your model