Answer:
To calculate the total cost of the brackets, before tax, we need to determine how many brackets are needed and what size they are.
Since the shelving is 10 feet long, we can divide it by the length of the brackets to find the number of brackets needed. However, we also need to consider the requirement that the brackets should be 1 foot from each end and no more than 24 inches apart. This means that we cannot use only 48-inch brackets, as they would leave a gap of more than 24 inches between the last bracket and the end of the shelf. Therefore, we need to use at least one 60-inch bracket, and the rest can be 48-inch brackets.
One possible arrangement is to use one 60-inch bracket in the middle, and two 48-inch brackets on each side, spaced 24 inches apart. This would satisfy the requirements and cover the entire length of the shelf. The total cost of this arrangement would be:
$\text{Total cost} = 1 \times \$16.95 + 4 \times \$12.95 = \$68.75$
Another possible arrangement is to use two 60-inch brackets, one at each end, and one 48-inch bracket in the middle. This would also satisfy the requirements and cover the entire length of the shelf. The total cost of this arrangement would be:
$\text{Total cost} = 2 \times \$16.95 + 1 \times \$12.95 = \$46.85$
Therefore, the minimum total cost of the brackets, before tax, is **\$46.85**. This is the optimal solution, as it uses the least number of brackets and the smallest total length of brackets. ️
