A person wants to plant two types of fruits, A and B, on farmland, and sets the planting area of fruit A (area A) and the planting area of fruit B (area B) to satisfy the following three conditions: (I) Area A does not exceed 15 hectares. (II) The sum of area A and area B does not exceed 24 hectares. (III) Area A does not exceed 3 times area B, and area B does not exceed 2 times area A. Let area A be $x$ hectares and area B be $y$ hectares. Given that when the farmland is harvested, fruit A yields a profit of 6 ten-thousand yuan per hectare and fruit B yields a profit of 7 ten-thousand yuan per hectare, find the maximum profit from planting both fruits in ten-thousand yuan. Show the calculation process in the solution area of the answer sheet, and draw the feasible region in the diagram area of the answer sheet, marking all vertices of the region and shading the region with diagonal lines.
A person wants to plant two types of fruits, A and B, on farmland, and sets the planting area of fruit A (area A) and the planting area of fruit B (area B) to satisfy the following three conditions:\\
(I) Area A does not exceed 15 hectares.\\
(II) The sum of area A and area B does not exceed 24 hectares.\\
(III) Area A does not exceed 3 times area B, and area B does not exceed 2 times area A.\\
Let area A be $x$ hectares and area B be $y$ hectares.
Given that when the farmland is harvested, fruit A yields a profit of 6 ten-thousand yuan per hectare and fruit B yields a profit of 7 ten-thousand yuan per hectare, find the maximum profit from planting both fruits in ten-thousand yuan. Show the calculation process in the solution area of the answer sheet, and draw the feasible region in the diagram area of the answer sheet, marking all vertices of the region and shading the region with diagonal lines.