Arley’s Bakery makes fat-free cookies that cost $1.60 each. Arley expects 40% of the cookies to fall apart and be discarded. Arley wants a 35% markup on cost and produces 200 cookies. Assume that Arley can sell the broken cookies for $1.50 each. What should Arley price each cookie? (Round your answer to the nearest cent.)
Well, Arley seems to have a bit of a crumbly situation on their hands! Let's break it down, shall we?
First, Arley expects 40% of the cookies to be discarded. That's a lot of cookie casualties! So out of the 200 cookies produced, 40% would be 80 cookies that are beyond saving. Poor little things.
Now, Arley can sell those broken cookies for $1.50 each. But wait... shouldn't Arley consider the cost of those cookies when pricing the good ones? Absolutely!
Arley wants a 35% markup on the cost, which means the desired selling price should be 135% of the cost. Let's calculate the cost:
The cost of each fat-free cookie is $1.60. Out of the 200 cookies, 80 will be thrown away, leaving 120 good cookies. So the cost would be 120 cookies multiplied by $1.60 each, which equals $192.
Now, let's calculate 135% of the cost:
135% of $192 is $259.20. But we need to take into account the discarded cookies too. So, we'll divide $259.20 by the 120 good cookies, which gives us $2.16 per cookie.
Therefore, Arley should price each cookie at $2.16 to achieve the desired markup and account for the discarded ones.
Hope that helps! Enjoy your cookies, but watch out for any crumbs!
To find the price each cookie should be priced, we need to consider the production cost, the discarded cookies, and the desired markup.
Step 1: Calculate the total cost per cookie
The cost of each fat-free cookie is $1.60.
Step 2: Calculate the number of discarded cookies
Arley expects 40% of the cookies to be discarded, so 40% of 200 cookies is 0.4 * 200 = 80 cookies.
Step 3: Calculate the price of the discarded cookies
The discarded cookies can be sold for $1.50 each.
The total cost of the discarded cookies is 80 * $1.50 = $120.
Step 4: Calculate the total cost of the remaining cookies
The total cost of the remaining 120 cookies (200 total - 80 discarded) is 120 * $1.60 = $192.
Step 5: Calculate the desired markup
Arley wants a 35% markup on cost, which means the selling price should include a 35% increase from the cost.
The markup amount is 35% of $192, which is 0.35 * $192 = $67.20.
Step 6: Calculate the selling price of each cookie
The total selling price should be the cost of the remaining cookies plus the desired markup: $192 + $67.20 = $259.20.
Step 7: Find the price per cookie
To find the price per cookie, divide the total selling price by the number of remaining cookies: $259.20 / 120 = $2.16.
Therefore, Arley should price each cookie at $2.16 (rounded to the nearest cent).
To determine the price at which Arley should sell each cookie, we need to take into account the cost, the expected discarded cookies, the desired markup, and the price at which the broken cookies can be sold.
First, let's calculate the total cost of producing the cookies:
Cost per cookie = $1.60
Next, we need to find the number of cookies that will be discarded:
Number of cookies = 200
Expected discarded cookies = 40% of 200 = 0.4 * 200 = 80 cookies
Now, let's calculate the total cost of the cookies, taking into account the discarded ones:
Total cost = (Number of cookies - Discarded cookies) * Cost per cookie
Total cost = (200 - 80) * $1.60 = 120 * $1.60 = $192
To determine the selling price, we need to add a 35% markup on the cost:
Markup percentage = 35%
Markup amount = Markup percentage * Total cost
Markup amount = 35% * $192 = 0.35 * $192 = $67.20
Now, we can calculate the total expected revenue:
Total revenue = Total cost + Markup amount
Total revenue = $192 + $67.20 = $259.20
Since there are 80 discarded cookies that can be sold for $1.50 each, the revenue from selling the discarded cookies is:
Revenue from discarded cookies = Discarded cookies * Price per discarded cookie
Revenue from discarded cookies = 80 * $1.50 = $120
To find the remaining revenue from the good cookies, we subtract the revenue from the discarded cookies from the total revenue:
Revenue from good cookies = Total revenue - Revenue from discarded cookies
Revenue from good cookies = $259.20 - $120 = $139.20
Finally, to determine the price per cookie, we divide the revenue from good cookies by the number of good cookies:
Price per cookie = Revenue from good cookies / Number of good cookies
Price per cookie = $139.20 / (Number of cookies - Discarded cookies)
Price per cookie = $139.20 / (200 - 80) = $139.20 / 120 ≈ $1.16
Therefore, Arley should price each cookie at approximately $1.16 each.
200 * 1.60 = $320 = Total cost.
Selling price = $P.
(0.4*200)cookies * 1.50/cookie = $120 Received for broken cookies.
(0.6*200)P + 120 = 1.35*320,
120P + 120 = 432, P = $2.60 each.