Bosley's Pet Foods buys dog kibbl for $19.50 per bag, less 40%. The store's overhead is 33 1/3% of the selling price, and the desired profit is 10% of the selling price.
(a) At what price per bag should the dog food be sold?
(b) At this price, what is the rate of markup on cost?
(c) What is the break-even price?
Arithmetic is used to solve the problem although algebra can also be used.
Cost price = $19.50- 19.50*0.40 = $11.70
The selling price includes
- 33 1/3 % of overhead
- 10 % of profit
So the fraction of cost in selling price
= 100% - 33 1/3 - 10 = 56 2/3%
Therefore selling price
= cost / fraction of cost
= $11.70 / (56 2/3%)
= $11.70 / (170/300)
= $11.70 * 300/170
= $20.65
Check:
Profit (10%) = 20.65*0.1 = $2.07
Overhead (33 1/3%) = 20.65*(1/3)= 6.88
Cost price = 20.65-2.07-6.88=11.70
So the answer is correct.
(b) the mark-up on cost is the profit divided by the cost price. It should be different from 33 1/3%.
(c) the break even price is the selling price less the profit, i.e. zero profit.
To solve this problem, we'll need to calculate the price per bag, the rate of markup on cost, and the break-even price. Let's break it down step-by-step.
Step 1: Calculate the selling price per bag.
Bosley's Pet Foods buys dog kibble for $19.50 per bag, less 40%.
Discount amount = 40% of $19.50 = $19.50 x 0.40 = $7.80
Cost of dog kibble after discount = $19.50 - $7.80 = $11.70
To find the selling price per bag, we need to factor in the overhead and desired profit.
Step 2: Calculate the selling price with overhead.
Overhead is 33 1/3% of the selling price.
Desired profit is 10% of the selling price.
Let x be the selling price per bag.
Overhead = 33 1/3% of x = (33 1/3 / 100) * x = (1/3) * x
Profit = 10% of x = (10/100) * x = (1/10) * x
Selling price per bag = Cost + Overhead + Profit
x = $11.70 + (1/3)x + (1/10)x
Now, we'll solve this equation to find the selling price per bag.
Step 3: Solve the equation for x.
Multiply through by 30 to eliminate the fractions:
30x = 30 * ($11.70 + (1/3)x + (1/10)x)
30x = 30 * $11.70 + 10x + 3x
30x = $351 + 13x
Rearrange the equation:
30x - 13x = $351
17x = $351
Solve for x:
x = $351 / 17 = $20.65
(a) The dog food should be sold at a price of $20.65 per bag.
Step 4: Calculate the rate of markup on cost.
Markup on cost = (Selling price per bag - Cost per bag) / Cost per bag
Markup on cost = ($20.65 - $11.70) / $11.70
Markup on cost = $8.95 / $11.70
(b) The rate of markup on cost is approximately 76.5%.
Step 5: Calculate the break-even price.
Break-even price is the price at which there is no profit or loss.
Break-even price = Cost + Overhead
Break-even price = $11.70 + (1/3) * $20.65 = $18.25
(c) The break-even price is $18.25 per bag.
To solve this problem, we need to follow a series of steps. Let's break it down step by step:
Step 1: Calculate the discounted price of the dog kibble.
Bosley's Pet Foods buys the dog kibble for $19.50 per bag and offers a 40% discount. To calculate the discounted price, we subtract 40% from the original price:
Discounted price = Original price - (Original price * Discount rate)
Discounted price = $19.50 - ($19.50 * 0.40)
Step 2: Determine the overhead cost.
The overhead cost is 33 1/3% of the selling price. To calculate the overhead cost, we multiply the discounted selling price by 33 1/3%:
Overhead cost = Discounted price * (33 1/3% / 100)
Step 3: Calculate the desired profit.
The desired profit is 10% of the selling price. To calculate the desired profit, we multiply the discounted selling price by 10%:
Desired profit = Discounted price * (10% / 100)
Step 4: Calculate the selling price per bag.
The selling price per bag can be obtained by summing up the discounted price, overhead cost, and desired profit:
Selling price per bag = Discounted price + Overhead cost + Desired profit
Step 5: Calculate the rate of markup on cost.
The rate of markup on cost is calculated by taking the difference between the discounted selling price and the cost price, and then dividing it by the cost price:
Rate of markup on cost = (Selling price per bag - Discounted price) / Discounted price
Step 6: Calculate the break-even price.
The break-even price is the minimum selling price at which the business covers all costs without making a profit. It is calculated by adding the overhead cost and the cost price:
Break-even price = Discounted price + Overhead cost
Now, let's perform the calculations:
(a) At what price per bag should the dog food be sold?
First, we calculate the discounted price:
Discounted price = $19.50 - ($19.50 * 0.40)
Next, we calculate the overhead cost:
Overhead cost = Discounted price * (33 1/3% / 100)
Then, we calculate the desired profit:
Desired profit = Discounted price * (10% / 100)
Finally, we calculate the selling price per bag:
Selling price per bag = Discounted price + Overhead cost + Desired profit
(b) At this price, what is the rate of markup on cost?
First, we calculate the rate of markup on cost:
Rate of markup on cost = (Selling price per bag - Discounted price) / Discounted price
(c) What is the break-even price?
First, we calculate the break-even price:
Break-even price = Discounted price + Overhead cost
Plug in the values for each of these steps to obtain the final answers.