1st) Find the 1st shaded region: 1st Quadrant since x≥0 and y≥0
2nd) Let's find the x and y intercepts of 2x+y = 6 x-intercepts for y = 0 , x=6 →A(3,0) y-intercepts for x = 0 , y =3→B(0,6) . Now Join AB 2nd shaded region
3rd) Let's find the x and y intercepts of x+2y = 6 x-intercepts for y = 0 , x=6 →C(6,0) y-intercepts for x = 0 , y =3→D(0,3) . Now Join CD 3rd shaded region
4th) Now let's calculate the coordinate of the intersection point of x+2y=6 and 2x+y =6 Solving it will give you x = 2 and y = 2 (coordinates of the intersection of AB with DC, le be E. (4th shaded region).
Re write all pairs:
A(3,6), B(0,6), C(6,0), D(0,3), E(2,2). Now plug in each pairs with the equation:
F= 5x + 2y
For A(3,6), →→F=15+12 = 25 For B(0,6), →→F=0+12 = 12 For C(6,0), →→F=30+0 = 30 For D(0,3), →→F=0+6 = 6 For E(2,2), →→F=20+4 = 14 So the max value of F= 5x+2y is 30 at C(6,0) Hope that I didn't make any mistake
<span>A) 3 - The third sock will match the first or second if they don't match each other. B) 14 - It's highly unlikely yet possible to remove all brown socks first, the next two would have to be black.</span>