Answer:
Step-by-step explanation:
Let's start with constraint 1: � + 2 � ≤ 8 x+2y≤8. We'll plot the line � + 2 � = 8 x+2y=8 and shade the region below it (since it's less than or equal to): The line � + 2 � = 8 x+2y=8 crosses the x-axis at (8,0) and the y-axis at (0,4). Let's plot these points and draw the line. Next, constraint 2: � − � ≤ − 2 x−y≤−2. Plot the line � − � = − 2 x−y=−2 and shade the region below it. The line � − � = − 2 x−y=−2 crosses the x-axis at (-2,0) and the y-axis at (0,2). Plot these points and draw the line. Now, let's plot the feasible region, which is the overlapping shaded area formed by the intersection of the shaded regions from constraints 1 and 2. Finally, we'll evaluate the objective function � = 2 � + 3 � P=2x+3y at the vertices of the feasible region to find the maximum value of � P. Once we find the maximum value of � P and the corresponding ( � , � ) (x,y) coordinates, we'll have our solution.
