Arley’s Bakery makes fat-free cookies that cost $1.60 each. Arley expects 25% of the cookies to fall apart and break. Assume that Arley can sell the broken cookies for $1.50 each. Arley wants a 55% markup on cost and produces 200 cookies. What price should Arley charge for each unbroken cookie? (Round your answer to the nearest cent.)
Number of cookies made --- 200
cost of cookies = 1.6(200) = $320
50 are broken and 150 are good
to have a 55% markup on cost, her return must be 1.55($320) = $496
let her selling price of good cookies be x
1.6(50) + 150x = 496
solve for x
To find the price that Arley should charge for each unbroken cookie, we need to calculate the total cost and then determine the markup.
Step 1: Calculate the total cost.
Arley's Bakery produces 200 cookies.
The cost of each cookie is $1.60.
So, the total cost of producing 200 cookies is 200 * $1.60 = $320.
Step 2: Calculate the expected loss on broken cookies.
Arley expects 25% of the cookies to be broken.
So, the number of broken cookies is 25% of 200, which is 0.25 * 200 = 50 cookies.
The expected loss on broken cookies is 50 * ($1.60 - $1.50) = $5.
Step 3: Calculate the total cost with the expected loss on broken cookies.
The total cost with the expected loss on broken cookies is $320 + $5 = $325.
Step 4: Calculate the selling price with a 55% markup on cost.
The markup on cost is 55% of $325, which is 0.55 * $325 = $178.75.
Step 5: Determine the price for each unbroken cookie.
To find the price for each unbroken cookie, we subtract the expected loss on broken cookies from the selling price with the markup.
The selling price for each unbroken cookie is $178.75 - ($5 / 200) = $178.75 - $0.025 = $178.725.
Rounded to the nearest cent, the price Arley should charge for each unbroken cookie is $178.73.
To find the price Arley should charge for each unbroken cookie, we need to consider the production cost, the expected breakage rate, the markup percentage, and the desired profit.
First, let's determine the total cost of producing the cookies:
Cost per cookie = $1.60
Next, we need to calculate the number of broken cookies:
Expected breakage rate = 25%
Number of cookies = 200
Number of broken cookies = 25% * 200 = 0.25 * 200 = 50 cookies
Now let's calculate the profit from selling the broken cookies:
Price per broken cookie = $1.50
Profit from selling broken cookies = Price per broken cookie * Number of broken cookies
Profit from selling broken cookies = $1.50 * 50 = $75
To achieve a 55% markup on cost, we need to calculate the total cost of producing the cookies, including the expected profit:
Total cost = Cost per cookie * Number of cookies + Desired profit
Total cost = $1.60 * 200 + Desired profit
Since the desired profit is not given, we'll use a trial and error method to find it.
Let's assume the desired profit is $X. Therefore:
Total cost = $1.60 * 200 + $X
To achieve a 55% markup on cost, the selling price would be:
Selling price = Total cost + Markup
Selling price = Total cost + 55% * Total cost
Selling price = Total cost * (1 + 0.55)
Selling price = Total cost * 1.55
Now we can set up an equation to solve for the desired profit:
Selling price = Total cost * 1.55
$X = ($1.60 * 200 + $X) * 1.55
Simplifying the equation:
$X = ($320 + $X) * 1.55
$X = $496 + $1.55X
Bringing the 'X' terms to one side:
$X - $1.55X = $496
-$0.55X = $496
X ≈ $-901 (rounded to the nearest cent)
Since the calculated desired profit is negative, it means that a 55% markup on cost is not achievable with the given information. However, we can still calculate the selling price by adding a reasonable desired profit, let's say $50 for example.
Total cost = $1.60 * 200 + $50 = $320 + $50 = $370
Now we can calculate the selling price per unbroken cookie with the reasonable desired profit:
Selling price = Total cost * 1.55 = $370 * 1.55 ≈ $573.50
Therefore, Arley should charge approximately $573.50 (rounded to the nearest cent) for each unbroken cookie.