There's only one constraint (apart from x and y both being positive) so we consider the x and y intercepts of 4x+7y=28. The feasibility region is to the right of this line. x intercept=28/4=7, y intercept=28/7=4. We need to know which intercept gives us the minimum c=5x+25y:
(7,0): c=35; (0,4): c=100. The minimum is when x=7, y=0.