A cardboard box without a lid is to have a volume of 16,384 cm3. Find the dimensions that minimize the amount of cardboard used. (Let x, y, and z be the dimensions of the cardboard box.)

The dimensions that minimize the amount of cardboard used is

x = 31 cm ,  y = 34 cm & Z = 15.54 cm

Step-by-step explanation:

Volume of the cardboard = 16,384

The function that represents the area of the cardboard without a lid is given by

------  (1)

Volume of the cardboard with sides x, y & z is

Put this value of z in equation (1) we get

Differentiate above equation with respect to x & y we get

Take

 ------ (2)

 ------- (3)

By solving equation (2) & (3) we get

x = 31 cm

From equation 2

y = 32768 ()

y = 34 cm

Z = 15.54 cm

Thus the dimensions that minimize the amount of cardboard used is

x = 31 cm ,  y = 34 cm & Z = 15.54 cm

step-by-step explanation:

given perimeter: 28cm

length: 9cm

atp,

2(l+w)=p of the reactangle

2(9+x)=28

18+2x=28

2x=28-18

x=10/2

x=5

therefore width is 5 cm