Answer:
dimensions to minimize cost is 6 inches x 6 inches x 6 inches
Step-by-step explanation:
Since the box has a square bottom, then it means length and width are the same value. Let the length and width be x. Let the depth by y.
Thus;
Volume is; V = x²y
We are given volume as 216 in³
Thus, V = 216
x²y = 216
y = 216/x²
Surface area of box will be;
S = 2x² + 4xy
Since box is to be made of sheet of paper that coast 1 cent per square inch.
It's means per Sq.m is $0.01
Thus;
C(x) = 2 × 0.01(x²) + 4 × 0.01(xy)
C = 0.02x² + 0.04xy
Put 216/x² for y;
C = 0.02x² + 0.04x(216/x²)
C = 0.02x² + 8.64/x
dC/dx = 0.04x - 8.64/x²
At dC/dx = 0, cost is minimum
Thus;
0.04x - 8.64/x² = 0
0.04x = 8.64/x²
x³ = 8.64/0.04
x³ = 216
x = 6
From y = 216/x²
y = 216/6²
y = 6
Thus,dimensions to minimize cost is 6 inches x 6 inches x 6 inches
Answer:
± 25
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
2x + 1 = 3x - 4
-2x -2x
--------------------
1 = x - 4
+4 +4
----------------
5 = x
The answer is 5.
Hope this helped.
Answer:
The answer to your question is L = 10 in , M = 9 in ; S = 5 in
Step-by-step explanation:
Data
longest side = 5 + x in
medium side = 4 + x in
shortest side = x
Perimeter = 24 in
Process
1.- Write and equation to solve this problem
Perimeter = longest side + medium side + shortest side
Substitution
24 = (5 + x) + (4 + x) + x
Simplification
24 = 5 + x + 4 + x + x
24 = 9 + 3x
24 - 9 = 3x
15 = 3x
x = 15/3
x = 5
2.- Calculate the lengths of the side
Longest side = 5 + 5 = 10 in
Medium side = 5 + 4 = 9 in
Shortest side = 5 in
