x+2y=>10 means x=>10-2y. Substitute this value in the second inequality: 20-4y+3y=>18. Subtract 18 from each side: 2-y=>0, so y<=2, and x=>10-2y so x=>10-4, and x=>6. We have to check out the inequalities for accuracy. We know that y must be between 0 and 2, inclusive; x must be greater than or equal to 6. The minimum value of y=0 and the maximum is 2 so when y is minimum, x is maximum and vice versa. The quantity 4x varies between 40 (y=0) and 24 (y=2) and 5y varies between 0 and 10. The quantity 4x+5y varies between 40 (x=10 and y=0) and (x=6 and y=2) and 34. So 34 is apparently the minimum value of c. Let's pick a y value between 0 and 2, and let's pick y=1. The minimum value of x is 8 and the minimum value of c is 37. Let's pick y=1/2, then min x=9 and c=38.5. Now pick y=3/2, so min x=7 and c=35.5.