Step-by-step explanation:
a.
x = number of matching questions
y = number of essay questions
x >= 3
x <= 12
y >= 4
y <= 15
x + y <= 20
the delimiter lines are therefore
x = 3
x = 12
y = 4
y = 15
y = 20 - x
when you graph these lines, the corners (intersection points) of the inner shaded area are
(3, 4)
(12, 4)
(3, 15)
(12, 8)
(5, 15)
the other intersection points
(12, 15)
(3, 17)
(16, 4)
are outside the inner shaded area.
b.
10x + 25y = score
and this we want to maximize.
we have to try the 5 corners from a. and see, which one gives the maximum score.
(3, 4) gives
10×3 + 25×4 = 30 + 100 = 130
(12, 4) gives
10×12 + 25×4 = 120 + 100 = 240
(3, 15) gives
10×3 + 25×15 = 30 + 375 = 405
(12, 8) gives
10×12 + 25×8 = 120 + 200 = 320
(5, 15) gives
10×5 + 25×15 = 50 + 375 = 425
that is the most.
so, Phil should do 5 matching questions and 15 essay questions for maximum score.
