Each of the four inequalities has an associated equation:
2x + 3y = 24, 3x + 2y = 36, x = 0 and y = 0
The graphs of these equations are lines.
x = 0 is the equation for the y-axis and y = 0 is the equation for the x-axis.
Graph the other two lines on the same graph.
The two lines graphed above plus the x and y axes should form some kind of quadrilateral in the first quadrant.
The points inside and along the edges of this quadrilateral are all the possible solutions which fit all four inequalities.
The quadrilateral has four vertices:
The origin, (0, 0)
The point where the line 3x + 2y = 36 intersects the x-axis.
The point where the line 2x + 3y = 24 intersects the y-axis.
The point where the lines 2x + 3y = 24 and 3x + 2y = 36 intersect each other.
Find the three unknown vertices.
Among all the solutions (the points along the edges and the points in the interior of the quadrilateral), the largest (and smallest) possible values for R will come from the coordinates of one of the vertices of the quadrilateral. So try the coordinates of each vertex, one vertex at a time, in the equation for R: R = 10x + 15y. This will result in an R for each vertex. One of them will be the largest possible value for R and one of them will be the smallest possible value for R. (Your post did not say which you were looking for, the largest/maximum or smallest/minimum value for R.)