Answer:
The gaph is shown in the image below
Step-by-step explanation:
Graph of Inequalities
Let's graph the region of the inequality
[tex]0.8m + 0.4p \leq 2,000[/tex]
Since there is no indication, we'll assume the variable p to be in the horizontal axis and m in the vertical axis. Let's solve for m
[tex]\displaystyle m=\frac{2,000-0.4p}{0.8}[/tex]
Since both m and p are positive, we can assume
[tex]2,000-0.4p\geq 0[/tex]
Or, equivalently
[tex]p \leq 5,000[/tex]
Thus, we can give p any value between 0 and 5,000 to get the corresponding values for m. Let's select the values p=0, p=1,000, p=5,000 to get the points
( 0 ; 2,500 ) ( 1,000 ; 2,000 ) ( 5,000 ; 0 )
With these points we can plot the line representing the function. To know which area must be shaded, we only need to test one point below or above the line. If it fulfills the inequality, then the whole area is shaded.
Let's test the point ( 1,000 ; 1,000 )
[tex]0.8\cdot 1,000 + 0.4\cdot 1,000 \leq 2,000[/tex]
[tex]1,200 \leq 2,000[/tex]
Since the condition is met, the area below the line must be shaded as the solution of the inequality
The gaph is shown in the image below
