Astorage box with a square base must have a volume of 90 cubic centimeters. the top and bottom cost $0.60 per square centimeter and the sides cost $0.30 per square centimeter. find the dimensions that will minimize cost. (let x represent the length of the sides of the square base and let y represent the height.

Answer-

For side length of 3.56 cm and height of 7.10 cm the cost will be minimum.

Solution-

Let us assume that,

x represents the length of the sides of the square base,

y represent the height.

Given the volume of the box is 90 cm³, so

As the top and bottom cost $0.60 per cm² and the sides cost $0.30 per cm². Total cost C will be,

Then,

As C'' has all positive terms  so, for every positive value of x (as length can't be negative), C'' is positive.

So, for minima C' = 0

Then,

Therefore, for side length of 3.56 cm and height of 7.10 cm the cost will be minimum.

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

step-by-step explanation: