UB Food Products has three processing plants $($A$,$ B and C$),$ where different variables of potato products are produced. Recently, the company has experienced a growth in its product demand, so it wants to buy potatoes from new farms. The company is considering six new farms with the following projected harvest:

Table $4-1$

Farm $123456$

Projected Annual Harvest

$($thousands of tons$)11\mathrm{.}210\mathrm{.}512\mathrm{.}89\mathrm{.}310\mathrm{.}89\mathrm{.}6$

The company currently has the following additional available production capacity $($tons$)$ at its three plants, which it wants to utilise:

Table $4-2$

Plant A B C

Available Capacity

$($thousands of tons$)121014$

The shipping cost per ton from the farms being considered for purchase to the plants are as follows:

Table $4-3$

Farm Plant $($Shipping costs, $/$ton$)$

A B C

$1181512$

$2131017$

$3161418$

$4191516$

$5171912$

$6141612$