Question 366385
The feasibility region is all the points inside and on the boundary of the quadrilateral having vertices or corner points  (0,0), (1,0), (3,8), (0,5).  By the fundamental theorem of linear programming the maximum and minimum will occur at the corner points.  
At (0,0), p = 0.
At (1,0), p = -21
At (3,8), p = -21*3 + 11*8 = -63 + 88 = 25
At (0,5), p= 55.
Thus the maximum of p is 55 and the minimum is -21.