A) System of inequalities
Income from babysitting: 6x
Income from tutoring: 10y
Goal for this week: at least $ 75 => 6x + 10y ≥ 75
Number of hours: maximum $20 => x + y ≤ 20
x and y have to be zero or positvie => x≥0 and y ≥ 0
Answer of part A.6x + 10y ≥ 75x+y ≤ 20x ≥ 0y ≥ 0Part B. Graph
The solution is a region closed by 4 lines and you can find it in the file attached.
In that graph:
1) the line x + y = 20 is the upper limit
2) the line 6x + 10 y = 75 is the lower incclined line
3) y = 0 is the botton horizontal line it is the x-axis
4) x = 0 is the left vertical line, in is the y-axis
Part C.
Use, for example the point (7,10).
It is in the region of the graph limited by the above equations.
It implies:
Number of hours worked = 7 + 10 = 17 which is less than 20.
Income: 6(7) + 10(10) = 42 + 100 = 142, which is greater than 75
Of course, both are greater than 0.
In this way we proved that the point (7,10) is a true solution for the model.
