Your class decides to publish a calendar to raise money. The initial cost, regardless of the number of calendars printed, is $900. After the initial cost, each calendar costs $1.50 to produce. What is the minimum number of calendars your class must sell at $6 per calendar to make a profit of at least $1200?

Question

Your class decides to publish a calendar to raise money. The initial cost, regardless of the number of calendars printed, is $900. After the initial cost, each calendar costs $1.50 to produce. What is the minimum number of calendars your class must sell at $6 per calendar to make a profit of at least $1200?

Answer 1

Revenue - Cost = 1200

Let N be the number produced (and sold)
The revenue is 6N.
The cost is 900 + 1.5 N.

1200 = 6 N - (900 + 1.5N)
= 4.5 N -900
4.5 N = 2100
N = 467
N has to be an integer, so you round to the next higher integer.
N=466 would result in a loss.

Answer 2

To determine the minimum number of calendars your class must sell, we need to calculate the total cost and the total revenue.

Let's denote:
C = number of calendars
TC = total cost
TR = total revenue

The total cost is composed of the initial cost ($900) plus the cost of producing each calendar ($1.50).

TC = $900 + ($1.50 * C)

The total revenue is the number of calendars sold (C) multiplied by the selling price ($6).

TR = $6 * C

To make a profit of at least $1200, the total revenue must exceed the total cost by at least $1200.

TR - TC ≥ $1200

Substituting the expressions for TR and TC:

$6 * C - ($900 + ($1.50 * C)) ≥ $1200

Now, we can simplify and solve the inequality:

$6C - $900 - $1.50C ≥ $1200
$4.50C - $900 ≥ $1200
$4.50C ≥ $2100
C ≥ $2100 / $4.50
C ≥ 466.67

Since we cannot sell a fraction of a calendar, the minimum number of calendars your class must sell to make a profit of at least $1200 is 467.

Answer 3

To find the minimum number of calendars your class must sell, we need to consider the initial cost and the production cost per calendar.

Let's denote:
C = Number of calendars
P = Profit

The profit made by selling each calendar is the selling price minus the production cost:
Profit per calendar = Selling price - Production cost
Profit per calendar = $6 - $1.50
Profit per calendar = $4.50

To find the number of calendars required to make a profit of at least $1200, we can use the following equation:

P ≥ 1200

We can express the total profit as:
Total profit = Profit per calendar * Number of calendars
1200 ≤ (6 - 1.50) * C

Simplifying the equation, we have:
1200 ≤ 4.50C

Now, let's solve for the minimum number of calendars your class must sell:

Divide both sides of the equation by 4.50:
1200/4.50 ≤ C
266.67 ≤ C

Since we cannot sell a fraction of a calendar, the minimum number of calendars your class must sell to make a profit of at least $1200 is 267 calendars.

Note: In real life, you cannot sell a fraction of a calendar, so you would need to round up to the nearest whole number.