The material used to make a storage box costs $1.25 per square foot. The boxes have the same volume. How much does a company save by choosing to make 50 of Box 2 instead of 50 of Box 1?
Box 1: 20x6x4 in
Box 2: 15x4x8 in
[2(20*6 + 20*4 + 6*4) - 2(15*4 + 15*8 + 4*8) ] * 1.25/144 = 0.2083 = 20.83¢
To find out how much the company saves by choosing to make 50 of Box 2 instead of 50 of Box 1, we need to calculate the cost difference between the two boxes.
First, let's calculate the surface area of each box:
Box 1:
Length = 20 inches
Width = 6 inches
Height = 4 inches
Surface Area = 2 * (Length * Width + Length * Height + Width * Height)
Surface Area = 2 * (20 * 6 + 20 * 4 + 6 * 4)
Surface Area = 2 * (120 + 80 + 24)
Surface Area = 2 * 224
Surface Area = 448 square inches
Box 2:
Length = 15 inches
Width = 4 inches
Height = 8 inches
Surface Area = 2 * (Length * Width + Length * Height + Width * Height)
Surface Area = 2 * (15 * 4 + 15 * 8 + 4 * 8)
Surface Area = 2 * (60 + 120 + 32)
Surface Area = 2 * 212
Surface Area = 424 square inches
Now, let's convert the surface area from square inches to square feet by dividing by 144 (since there are 144 square inches in 1 square foot).
Box 1: 448 square inches / 144 = 3.11 square feet
Box 2: 424 square inches / 144 = 2.944 square feet
Next, let's calculate the cost of making each box:
Box 1: 3.11 square feet * $1.25 per square foot = $3.8875
Box 2: 2.944 square feet * $1.25 per square foot = $3.68
Now, let's calculate the cost difference for making 50 boxes:
Cost difference = (cost of 50 Box 2) - (cost of 50 Box 1)
Cost difference = (50 * $3.68) - (50 * $3.8875)
Cost difference = $184 - $193.875
Cost difference = -$9.875
Therefore, the company actually spends $9.875 more by choosing to make 50 of Box 2 instead of 50 of Box 1.
To determine the savings by choosing to make 50 of Box 2 instead of 50 of Box 1, we need to calculate the cost difference between the two boxes.
First, let's find the volume of each box:
Volume of Box 1 = length × width × height = 20 × 6 × 4 = 480 in³
Volume of Box 2 = length × width × height = 15 × 4 × 8 = 480 in³
Since both boxes have the same volume, the cost difference will depend on the surface area of the boxes.
To find the surface area of each box, we need to calculate the area of each face and then sum them up.
Surface area of Box 1:
Front and back faces: 20 × 6 = 120 in²
Side faces: 20 × 4 + 20 × 4 = 160 in²
Top and bottom faces: 6 × 4 + 6 × 4 = 48 in²
Total surface area of Box 1: 120 + 160 + 48 = 328 in²
Surface area of Box 2:
Front and back faces: 15 × 4 = 60 in²
Side faces: 15 × 8 + 15 × 8 = 240 in²
Top and bottom faces: 4 × 8 + 4 × 8 = 64 in²
Total surface area of Box 2: 60 + 240 + 64 = 364 in²
Now, let's calculate the cost difference:
Cost of Box 1 = Surface area of Box 1 × Cost per square foot
Cost of Box 2 = Surface area of Box 2 × Cost per square foot
Savings = Cost of Box 1 - Cost of Box 2
Since the cost of material is given as $1.25 per square foot, we can substitute:
Savings = (Surface area of Box 1 × $1.25) - (Surface area of Box 2 × $1.25)
Savings = ($1.25 × 328 in²) - ($1.25 × 364 in²)
Savings = $410 - $455
Savings = -$45
Therefore, the company would incur an additional cost of $45 by choosing to make 50 of Box 2 instead of 50 of Box 1.