A rectangular box with a volume of 320 ft^3 is to be constructed with a square base and top. The cost per square foot for the bottom is $15; for the top it is $10; and the sides are $2.50. What dimensions will minimize the cost?
I am absolutely stuck on what to do. From what I have tried figuring out, I have this.
Length x Width x Height = Volume (320 ft^3)
I believe the volume equation is (x^2)y = 320 which can also be y = 320/(x^2)
I have no idea if this is correct, but I think the cost equation is 15x^2 + 10x^2 + 2.5(4)xy = Cost
If I plug what I solved to be y (above) into the cost equation, I can simplify it into...
25x^2 + 10x[320/(x^2) which also equals 25x^2 + 3,200x/(x^2)
Simplified further you have 3,200x/(x^2) = -25x^2
and further 3,200x = -25x^4 which further is 128 = -x^3
That's as far as I got, and I have no idea what to do now. PLEASE HELP.
I am absolutely stuck on what to do. From what I have tried figuring out, I have this.
Length x Width x Height = Volume (320 ft^3)
I believe the volume equation is (x^2)y = 320 which can also be y = 320/(x^2)
I have no idea if this is correct, but I think the cost equation is 15x^2 + 10x^2 + 2.5(4)xy = Cost
If I plug what I solved to be y (above) into the cost equation, I can simplify it into...
25x^2 + 10x[320/(x^2) which also equals 25x^2 + 3,200x/(x^2)
Simplified further you have 3,200x/(x^2) = -25x^2
and further 3,200x = -25x^4 which further is 128 = -x^3
That's as far as I got, and I have no idea what to do now. PLEASE HELP.