Michelle has $8 and wants to buy a combination of dog food to feed at least two dogs at the animal shelter. A serving of dry food costs $1, and a serving of wet food costs $3. This system of inequalities models the scenario:

x + 3y ≤ 8
x + y ≥ 2

Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)

Part B: Is the point (8, 2) included in the solution area for the system? Justify your answer mathematically. (3 points)

Part C: Choose a point in the solution set and interpret what it means in terms of the real-world context. (3 points)

Part A: Please find the included graph of the system of inequalities

The solution set are y ranges from 0 to 8/3 and x ranges from 0 to 8

Part B: The point (8, 2) is not included in the solution area for the system

Part C: At the point (2, 2) Michele is able to feed four dogs two dry foods and two we t foods for $8

Step-by-step explanation:

Part A: The expression given are;

1) x + 3y ≤ 8..........................(1)

2) x + y ≥ 2...........................(2)

We rearrange inequality (1) and rewrite it in an equation format to make y the subject of the formula so we have;

3y = 8 - x

y = 8/3 - x/3

Which gives;

y ≤ 8/3 - x/3

Similarly for equation (2), we have;

y = 2 - x

Which gives;

y ≥ 2 - x

After plotting, we shade below the plotted solid line for y = 8/3 - x/3 and above the plotted solid line for y = 2 - x to get the regions of the inequality y ≤ 8/3 - x/3 and y ≥ 2 - x respectively

The solution set are y ranges from 0 to 8/3 and x ranges from 0 to 8

Part B: For x = 8 and y = 2 we have for inequality (1)

8 + 3 × 2 = 14 8, therefore, the point (8, 2) is not included in the solution area for the system

Also from the shaded region on the graph, it is shown that the point (8, 2) is not included in the solution area for the system

Part C: The point chosen is (2, 2)

It means that Michelle will buy 2 servings of dry food for 2 × $1 ( which makes $2) and 2 servings of wet food for 2 × $3 ( which is $6)  for a total of $8 to feed four dogs.

a. -0.3 > -0.33