Step-by-step explanation:
The system of inequalities can be written as:
a ≥ 2 (buy at least 2 hotdogs)
a + y ≥ 12 (buy no less than 12 hotdogs and drinks altogether)
4.5a + 1.75y ≤ 35 (stay within the budget of $35)
To solve this graphically, we can plot the boundary lines for each inequality and shade the feasible region where all three conditions are satisfied.
First, plot the boundary line for a = 2. This is a vertical line passing through a = 2 on the x-axis.
Next, plot the boundary line for a + y = 12. This is a diagonal line passing through (0,12) and (12,0) on the coordinate plane.
Finally, plot the boundary line for 4.5a + 1.75y = 35. This is a diagonal line passing through (7.78, 0) and (0, 20) on the coordinate plane. (To find these points, solve for a or y in terms of the other variable and substitute values to get two points.)
The feasible region is the shaded area where all three boundary lines intersect. One possible solution within this region is (a=6, y=6). Julian could buy 6 hotdogs and 6 drinks for a total cost of $33, which is within his budget of $35.