Atrash company is designing an open-top, rectangular container that will have a volume of 3645 ft cubed. the cost of making the bottom of the container is $5 per square foot, and the cost of the sides is $4 per square foot. find the dimensions of the container that will minimize total cost.

L=9.3 ft

b=9.3 ft

h=42.14 ft

Step-by-step explanation:

Given

volume(V)=

let L,b,h be length ,breadth and height of cube

Bottom cost=5Lb

Side Costs=8Lh+8bh

Total cost(C)=5Lb+8Lh+8bh

C=

considering to be fixed ,cost become the function of L+b

and if h is fixed then Lb is also fixed and for cost to be minimum L+b should be minimum therefore L=b is necessary

thus

C=

For minimum cost differentiate w.r.t b

L=9.3 ft

h=42.14 ft

60

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x