A store has two types of animal feed available. Type A contains 9 pounds of oats and 2 pounds of corn per bag. Type B contains 4 pounds of oats and pounds of corn per bag. A farmer wants to combine the two types so that the resulting mixture has at least 46 pounds of oats and at least 24 pounds of corn. The store only has 12 bags of type A feed and 14 bags of type B feed in stock. Type A costs $3 per bag, and type B costs $4 per bag. How many bags of each type should the farmer buy to minimize her cost?

Please write the problem solution in the solution text box; do not attach files.

Also, do not post short title without the actual solution (to be appended later). Post the answer right away. I need the answers with all the steps (including equations) shown. Do not include the Problem text before your answer unless you are quoting it in the answer you provide. Thanks!