A doughnut shop at a shopping mall sells a dozen doughnuts for $2.95. Beyond the fixed costs of $150 per day, it costs $1.45 for enough materials and labor to produce each dozen doughnuts. If the daily profit varies between $50 and $200, between what levels (in dozens) do the daily sales vary?

$50 < 2.95x -(1.45x + 150) < $200,

50 < 2.95x - 1.45x - 150 < 200,
50 < 1.5x - 150 < 200,
50 + 150 < 1.5x < 200+ 150,
200 < 1.5x < 350,
133.3 < X < 233.3.

So the sales was greater than 133.3 dozens but less than 233.3 dozens.
In other words, the sales varied
between 133.3 and 233.3 dozens.

Deez nuts

To find the range of daily sales in dozens, we need to calculate the number of dozens sold at the minimum and maximum profit levels.

Let's start with the minimum profit:

Profit = Revenue - Costs
Profit = (Price per dozen * Number of dozens) - (Fixed costs + Variable costs)

Given:
Profit = $50
Price per dozen = $2.95
Fixed costs = $150
Variable costs = $1.45 per dozen

Substituting the values into the profit equation, we can solve for the number of dozens:

$50 = ($2.95 * Number of dozens) - ($150 + $1.45 * Number of dozens)

Simplifying the equation, we get:

$50 = $2.95 * Number of dozens - $150 - $1.45 * Number of dozens
$50 + $150 = $2.95 * Number of dozens - $1.45 * Number of dozens
$200 = $1.50 * Number of dozens

Dividing both sides by $1.50, we find:

Number of dozens = $200 / $1.50
Number of dozens = 133.33

Since selling a non-integer number of dozens doesn't make sense, we can round down to the nearest whole number:

Number of dozens = 133 (minimum daily sales)

Now let's calculate the maximum daily sales:

Profit = $200

$200 = ($2.95 * Number of dozens) - ($150 + $1.45 * Number of dozens)

Simplifying:

$200 = $2.95 * Number of dozens - $150 - $1.45 * Number of dozens
$200 + $150 = $2.95 * Number of dozens - $1.45 * Number of dozens
$350 = $1.50 * Number of dozens

Dividing both sides by $1.50:

Number of dozens = $350 / $1.50
Number of dozens = 233.33

Again, we round down to the nearest whole number:

Number of dozens = 233 (maximum daily sales)

Therefore, the daily sales vary between 133 dozens and 233 dozens.

To determine the range of daily sales in dozens, we need to consider the fixed costs, variable costs, and profit for each scenario.

Let's calculate the profit per dozen doughnuts:

Profit per Dozen Doughnuts = Selling Price - (Variable Cost + Fixed Cost)

Profit per Dozen Doughnuts = $2.95 - ($1.45 + $150)

Profit per Dozen Doughnuts = $1.50 - $151.45

Profit per Dozen Doughnuts = -$149.45

Since the profit per dozen doughnuts is negative, it suggests that the doughnut shop is making a loss on each dozen sold. Therefore, it is not feasible to sell less than a dozen doughnuts.

Now, let's determine the range of daily sales that would result in a profit between $50 and $200.

Profit = (Profit per Dozen Doughnuts) x (Number of Dozens Sold)

To calculate the number of dozens sold, we rearrange the equation:

Number of Dozens Sold = Profit / Profit per Dozen Doughnuts

For a profit of $50:

Number of Dozens Sold = $50 / (-$149.45) [using the profit per dozen doughnuts calculated earlier]

Number of Dozens Sold = -0.34 (approximately)

Since the number of dozens cannot be negative, we round it up to the nearest whole number:

Number of Dozens Sold = 1 dozen (approximately)

For a profit of $200:

Number of Dozens Sold = $200 / (-$149.45) [using the profit per dozen doughnuts calculated earlier]

Number of Dozens Sold = -1.34 (approximately)

Since the number of dozens cannot be negative, we round it up to the nearest whole number:

Number of Dozens Sold = 2 dozens (approximately)

Therefore, based on the given information, the daily sales of the doughnut shop vary between approximately 1 and 2 dozens.