Question $2$: $(30\backslash \%)$

SA Food Products Company owns several farms where it grows and harvests potatoes. It then ships these potatoes to three processing plants $($called A$,$ B$,$ C$)$ where different varieties of potato products, including chips, are produced. Recently, the company has experienced a growth in its product demand so it wants to buy one or more new farms to produce more potato products. The company is considering six new farms with the following annual fixed costs and projected harvest.

The company currently has the following additional available production capacity $($tons$)$ at its three plants that it wants to use: Plant A: $12$ thousands of tons, Plant B: $10$ thousands of tons, Plant C: $14$ thousands of tons. The shipping costs $(\backslash$$$)$ per ton from the farms being considered for purchase to the plants are as follows:

The company wants to know which of the six farms it should purchase that will meet available production capacity at the minimum total cost, including annual fixed costs and shipping costs.

Formulate a mathematical model and solve it using a computer, and what is the optimal solution?