Question

Calculus Help?

Answer 1

The top and bottom margins of the poster = 4 cm

Side margins of the poster = 5 cm

w = width of printed area

h = Height of printed area

Area of the printed material on the poster wh= 390 cm²

Width of poster  = a + 2*4 = w + 10

Height of poster  = a + 2*5 = h + 8

Dimensions of the poster area with smallest area A = ?

A = (w + 10 )(h + 8)

Substitute : wh= 390 ⇒ h = 390/w

A = (w + 10 )(390/w + 8)

A = (w + 10 )(390 + 8w)/w

A = (390w + 8w² + 390*10 + 80w)/w

A = ( 8w² + 470w +  + 3910 )/w

A =  8w + 470 +  + 3910/w

Apply derivative both sides with respect to w

dA/dw =  8 + 3910(-1/w²)

dA/dw =  8 - 3910/w²

But area is constant : dA/dw = 0

0  =  8 - 3910/w²

 

3910/w² = 8

w² = 3910/8

w² = 488.75

w = 22.11 cm

wh= 390 ⇒ h = 390/w

h = 390/22.11

h = 17.64 cm

Solution :

Width of the poster smallest area is 22.11 cm

Height of the poster smallest area is 17.64 cm