MATH SOLVE

10 months ago

Q:
# ) The Home Depot purchases garden sheds for $1,000 less discounts of 40% and
20% and then sells them at a 100% markup on cost percentage. Seasonally,
these sheds sell for full price initially followed by a reduced price and then are
blown out at 50% off the regular price. Past experience indicates that 60% of
the sheds sell at full price, 30% at the reduced price, and 10% at the blowout
price. What should the reduced price be set at to achieve a maintained markup
of $360?

Accepted Solution

A:

To solve this problem, we can break it down into several steps:
Step 1: Calculate the cost of the garden sheds after discounts
The original price of the garden shed is $1000. With a 40% discount, the price becomes:
$1000 x (1 - 0.40) = $600
With another 20% discount, the price becomes:
$600 x (1 - 0.20) = $480
So the cost of each garden shed is $480.
Step 2: Calculate the selling price of the garden sheds
The markup on cost percentage is 100%. This means that the selling price is twice the cost. Therefore, the selling price of each garden shed is:
$480 x 2 = $960
Step 3: Calculate the revenue from each garden shed at each price point
At full price, each garden shed sells for $960, and 60% of the sheds are sold at this price. Therefore, the revenue from each shed sold at full price is:
$960 x 0.6 = $576
At the reduced price, each garden shed sells for a certain amount, which we'll call "x". 30% of the sheds are sold at this price. Therefore, the revenue from each shed sold at the reduced price is:
$x x 0.3
At blowout price, each garden shed sells for half the full price, which is $480. 10% of the sheds are sold at this price. Therefore, the revenue from each shed sold at blowout price is:
$480 x 0.1 = $48
Step 4: Set up an equation for the revenue
To achieve a maintained markup of $360, we want the total revenue from selling the garden sheds to be $360 more than the cost of purchasing them. The cost of purchasing each shed is $480, and there are a total of 100 sheds (since we are dealing with percentages, we can assume there are 100 sheds without loss of generality). Therefore, the cost of purchasing all the sheds is:
$480 x 100 = $48,000
To achieve a maintained markup of $360, the total revenue must be:
$48,000 + $360 = $48,360
We can set up an equation for the revenue from selling the sheds as follows:
$576 + $0.3x + $48 = $48,360
Simplifying this equation, we get:
$0.3x = $47,736
x = $159,120
Step 5: Interpret the result
The reduced price should be set at $159,120 to achieve a maintained markup of $360. This means that the revenue from selling each garden shed at the reduced price should be $159,120 / 30%, or $530.40. This price, combined with the revenue from selling the sheds at full price and blowout price, should result in a total revenue of $48,360, which is $360 more than the cost of purchasing the sheds.