Answer to Question #342406 in Calculus for yousii

Question

A poster is to have an area of 630 cm² with 2.5 cm margins at the bottom and sides and a 5 cm margin at the top. Find the exact dimensions (in cm) that will give the largest printed area.

width  = cm

height = cm

Answer 1

S=630 cm²

S=a*b, b=630/a

S= (2.5 *2 +a)*(7.5+b)

S= (5+a)*(7.5 + 630/a)= (37.5+3150/a+7.5a+630)=7.5a+3150/a+667.5

we find the first derivative and equate it to zero

S'= 7.5-3150a²=0

we solve the resulting equation and find the roots of the equation (i.e. the value of the unknown at which the value of the function (derivative) is 0). This will be the answer, i.e. the length of the side at which the area will be the largest.

7.5a²=3150

a²=420

a= 20.5; -20.5

width  = 20.5 cm

height = 30.7 cm

20.5 * 30.7 = 629.35 cm²