Mixed$-$Integer Programming $(15$ points$)$

Rockville$$s Best $($RB$)$ owns farms in Maryland where it grows and harvests strawberries. It then ships the

strawberries to three plants located in Annapolis, Baltimore and Fredrick for processing and packing.

The company has experienced recent growth and intends to expand its production by buying one or

more farms in Maryland. There are six new farms RB is considering. For strategic reasons, the company

has determined that it should treat farms $4$ and $5$ as a package deal $$ either buy both or buy neither.

The fixed annual cost and projected annual harvest of the farms as well as the shipping costs to the

plants and the plant capacities are given below:

Shipping costs, $$/$ton

Farm

Fixed Annual Costs

$($in $$1000$s$)$

Projected Annual Harvest

$($thousands of tons$)$ Annapolis Baltimore Frederick

$1$ $$40511\mathrm{.}2181512$

$2$ $$39010\mathrm{.}5131017$

$3$ $$45012\mathrm{.}8161418$

$4$ $$3689\mathrm{.}3191516$

$5$ $$52010\mathrm{.}8171912$

$6$ $$4659\mathrm{.}6141612$

Available Capacity

$($in thousands of tons$)121014$

Using the IBM$-$ILOG$-$CPLEX Optimization Studio determine the least cost optimal mix of farms that

Rockville$$s Best should buy to support its growth plans?

Please submit your $.$mod file. In addition, please indicate your solution as a tab in the excel spreadsheet.