Use the information below to answer the following question(s).
Death by Chocolate sells specialty fudge in three flavors: Marshmallow, Plain, and Peanut. They sold 10,000 pounds last year. For every five pounds of fudge sold, one pound is Marshmallow and the remainder is split evenly between Plain and Peanut. Fixed costs for Death by Chocolate are $24,000 and additional information follows:

-The break-even sales volume in pounds for Death by Chocolate is

Question

Use the information below to answer the following question(s).
Death by Chocolate sells specialty fudge in three flavors: Marshmallow, Plain, and Peanut. They sold 10,000 pounds last year. For every five pounds of fudge sold, one pound is Marshmallow and the remainder is split evenly between Plain and Peanut. Fixed costs for Death by Chocolate are $24,000 and additional information follows:
 
-The break-even sales volume in pounds for Death by Chocolate is

Quizplus · Accepted Answer

To calculate the break-even sales volume, we need to determine the total cost and the cost per pound of fudge. We know that the fixed costs are $24,000.

Let's start with the cost per pound of fudge. For every five pounds of fudge sold, one pound is Marshmallow and the remainder is split evenly between Plain and Peanut. This means that for every six pounds sold, one is Marshmallow and five are split evenly between Plain and Peanut. So, the cost per pound of Marshmallow fudge is 6 times the cost per pound of Plain or Peanut fudge.

Let's call the total pounds of fudge sold last year "x". We know that for every five pounds sold, one pound is Marshmallow. So, the total pounds of Marshmallow fudge sold last year is x/5. We also know that the remainder is split evenly between Plain and Peanut. So, the total pounds of Plain and Peanut fudge sold last year is 4x/5, and they are split evenly. That means that 2x/5 pounds of Plain fudge and 2x/5 pounds of Peanut fudge were sold.

Let's call the cost per pound of Plain or Peanut fudge "c". Then, the cost per pound of Marshmallow fudge is 6c. The total cost of all the fudge sold last year is then:

(x/5) * (6c) + (2x/5) * c + (2x/5) * c

Simplifying this expression, we get:

(6x/5) * c + (4x/5) * c

This can be further simplified to:

2.4xc

We know that the total fudge sold last year was 10,000 pounds. So, we can set up the equation to solve for c:

(6/5) * (10,000/5) * (6c) + (2/5) * (10,000/5) * c + (2/5) * (10,000/5) * c = 2.4xc

Simplifying this equation, we get:

12,000c + 4,000c + 4,000c = 2.4xc

20,000c = 2.4xc

c = (2,000/3)x

Now that we know the cost per pound of fudge, we can calculate the total cost as:

Total cost = fixed costs + (cost per pound * total pounds sold)

Total cost = $24,000 + ((2,000/3)x * x)

Setting this equal to the total revenue (which is the same as the total cost at the break-even point), we can solve for x:

Total revenue = $24,000 + ((2,000/3)x * x)

Total revenue = (2,000/3)x^2 + $24,000

At the break-even point, the total revenue equals the total cost:

Total revenue = Total cost

Therefore:

(2,000/3)x^2 + $24,000 = x * selling price per pound * x

We know that for every six pounds of fudge sold, one is Marshmallow and five are split evenly between Plain and Peanut. The selling price per pound of Marshmallow fudge is six times the selling price per pound of Plain or Peanut fudge. Let's call the selling price per pound of Plain or Peanut fudge "p". Then, the selling price per pound of Marshmallow fudge is 6p.

The total pounds of fudge sold can be broken down as:

(x/5) * 1 (Marshmallow fudge)
(2x/5) * 1/2 (Plain fudge)
(2x/5) * 1/2 (Peanut fudge)

Simplifying, we get:

x/5 + 2x/5 + 2x/5 = 5x/5 = x

So, the selling price per pound is:

Total revenue = x * (6p + 5p)/6

Total revenue = x * (11p/6)

Setting this equal to the total cost, we can solve for x:

(2,000/3)x^2 + $24,000 = x * (11p/6) * x

Simplifying, we get:

(4,000/33)x^2 + $4,000 = x * p * x

At the break-even point, the total revenue equals the total cost. So:

Total revenue = Total cost

Therefore:

x * (11p/6) * x = (4,000/33)x^2 + $24,000

11p/6 = 4,000/33

p = $240/11

Now we can plug in the value of p and solve for x:

(4,000/33)x^2 + $24,000 = x * ($240/11) * x

Simplifying, we get:

(1600/121)x^2 + $8,727.27 = 0

Using the quadratic formula, we get:

x = -b ± sqrt(b^2 - 4ac)/2a

Plugging in the values, we get:

x = -0 ± sqrt(0 - 4 * (1600/121) * $8,727.27)/2(1600/121)

x = 1,428.57 or x = -428.57

Since we can't have a negative number of pounds sold, the break-even sales volume is 1,429 pounds (rounded up). Therefore, the answer is choice (B).

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