If a=volume of 9% solution and b=volume of 24% solution:
a+b≤250mL total volume.
Amounts of pure salt in ingredients: 0.09a and 0.24b.
Amount of pure salt in mixture: 0.18(a+b).
0.09a+0.24b≥0.18×250, 0.09a+0.24b≥45.
a is the horizontal axis and b the vertical axis.
The graph shows a+b≤250 as the red shaded region and 0.09a+0.24b≥45 as the blue shaded region. Note that a, b≥0.
The boundaries are represented by the vertices of the triangular region: (0,187.5), (100,150), (0,250). These represent (a,b) values.
The point (100,150) where the lines intersect represents optimal values: a=100mL, b=150mL.
100mL of 9% solution=9mL of pure salt; 150mL of 24% solution=36mL of pure salt. Total amount of pure salt in mixture=45mL, which is 45/250=18%.
The two regions overlap as shown, and it is the triangular region which represents all solutions to the inequalities.
