Question

Please help I am so lost and confused thank you guys.

Answer 1

Explanation:

6) The inequalities are

x + y ≥ 60
`-eq\textcircled{1}`

400x + 1200y ≤ 68000
`-eq\textcircled{2}`

y ≥ 3x
`-eq\textcircled{3}`

x ≥ 0

y ≥ 0

P = 1900x + 14500y

7)

Intersection of eq(1) and eq(2)

x + y ≥ 60

⇒ y ≥ 60 - x

sub in eq(2)

400x + 1200(60 - x) = 68000

⇒ 400x + 72000 - 1200x = 68000

⇒ 72000 - 68000 = 1200x - 400x

⇒ 4000 = 800x

⇒ x = 4000/800

⇒ x = 5

sub in y ≥ 60 - x

y ≥ 60 - 5

y ≥ 55

Point1 (5, 55)

Intersection of eq(1) and eq(3)

x + y ≥ 60

y ≥ 3x

sub (3) in (1)

x + (3x) = 60

⇒ 4x = 60

⇒ x = 60/4

⇒ x = 15

sub in y ≥ 3x

y ≥ 3(15)

y ≥ 45

Point2 (15, 45)

Intersection of eq(2) and eq(3)

400x + 1200y ≤ 68000

y ≥ 3x

sub (3) in (2)

400x + 1200(3x) = 68000

⇒ 400x + 3600x = 68000

⇒ 4000x = 68000

⇒ x = 68000/4000

⇒ x = 17

y ≥ 3x

y ≥ 3(17)

y ≥ 51

Point3 (17, 51)

The three vertices are (5, 55), (15, 45) and (15, 45)

8) P = 1900x + 14500y

at Point1, P = 1900(5) + 14500(55) = 807000

at Point2, P = 1900(15) + 14500(45) = 681000

at Point3, P = 1900(17) + 14500(51) = 771800

The maximum is: P = 807000 when x = 5 and y = 55

9) The maximum number of people exposed to the ad is 807000, when there are 5 radio ads and 55 tv ads