Toy Manufacturer's Block Production: Optimal Paint Usage
How can the production team minimize paint usage for the blocks?
a. What is the expression for the minimum amount of paint needed for one block with edge b?
b. What if the team decides to use two coats of paint for each block?
c. How can the maximum length of edge b be determined when using two coats of paint?
Answers:
a. The expression for the minimum amount of paint needed for one block with edge b is 6b^2.
b. If the team uses two coats of paint, the expression changes to 12b^2.
c. The maximum length of edge b that can be used when applying two coats of paint is approximately 2.58 inches.
In order to minimize paint usage for the blocks, the production team needs to consider the surface area of the blocks and the number of coats of paint used. By calculating the surface area of each block and determining the amount of paint needed per block, the team can optimize their paint usage.
Minimum Paint Usage for One Block:
When using one coat of paint for each block, the expression representing the minimum amount of paint needed is 6b^2. This accounts for the surface area of all six faces of the block.
Increasing Paint Usage to Two Coats:
If the production team decides to use two coats of paint for each block, the minimum amount of paint needed per block increases to 12b^2. This ensures full coverage of the block with the additional coat of paint.
Determining Maximum Length of Edge b:
With each can of paint covering 60in^2, the maximum length of edge b can be calculated by setting up an inequality. The maximum length is approximately 2.58 inches to ensure that two coats of paint can cover the block adequately.