he length of a rectangular box is to be twice its width, and its volume is to be 40 ft3..... Full Question Below

Question

he length of a rectangular box is to be twice its width, and its volume is to be 40 ft³. The material for the base costs 45¢/ft², the material for the sides costs 10¢/ft², and the material for the top costs 20¢/ft². Letting x denote the width of the box, find a function in the variable x giving the cost C(x) (in cents) of constructing the box.

C(x) = 

65x2+1600x

 

 

Answer 1

C(x)= 280x^2

L = 2w V = 40 ft^3 = hLw = 2hw^2

hw^2 = 20 = hx^2 = 20

h=5, w=x=2, L=4

cost of base = 45 cents per square foot

cost of top = 20 cents per square foot

cost of sides = 10 cents per square foot

base = Lx = top=8 ft^2

sides = hL = 2hx =20 ft^2

and hx= 10 ft^2

2hL + 2hx = 4hx +2hx = 6hx= 60 ft^2

C(x)=C(8)= 45(8)+ 60(10)+20(8)= 600+65(8)=600+520=1120 cents= $11.20

h=2.5x

L=2x

C(x)= 65(2x^2)+60(2.5x^2)= (130+150)x^2= 280x^2

C(2)= 280(2^2)= 1120 cents

C(x)= 280x^2

which also = 65x^2 + 215x^2 = 65x^2 +430x

you were off with 65x^2 +1600x by 1170x