Question 85263
You need to test the extreme or "corner" points. These are (8 , 0) [8 is the biggest value x can be according to the first constraint, which in turn would make y = 0] , (0 , 24) [24 is the biggest value y can be according to the first constraint, which in turn would make x = 0] , (11 , 0) [11 is the biggest value x can be according to the second constraint, which in turn would make y = 0] , (0 , 16.5) [16.5 is the biggest value y can be according to the second constraint, which in turn would make x = 0]. Now, (0 , 24) doesn't conform to the second constraint and (11 , 0) doesn't conform to the first constraint, so they can be ruled out. So you need to plug in (8 , 0) and (0 , 16.5) into the expression 4x + 10y to get the respective values for z in each case:

4(11) + 10(0) = 44
4(0) + 10(16.5) = 165
44 is the smallest, so the answer is C.