Quickprint Services operates several franchise where it prints brochures, business cards, and stationery. It plans to sell 80 jobs next week, at an average cost of $52 each. Its weekly expenses are $1840
a.	How much must Quickprint charge for each job to break even?
b.	If it wishes to make a profit of $1200, what price does it have to charge?
c.	If it sells 90 jobs at the price determined in part (b), how much profit will be realized?
d.	If Quickprint sells 100 jobs through a special promotion, what is the minimum price it could charge to break even?


Let's break down the problem systematically and solve each part step by step.

### Given Information:
- Quickprint plans to sell **80 jobs** next week.
- The **average cost** of each job is **$52**.
- The **weekly expenses** are **$1840**.

### (a) Break-Even Price

At the break-even point, Quickprint's **revenue** must equal its **expenses**. Let’s determine the price per job they need to charge to cover their costs.

1. Let $ P $ be the price per job.
2. The total revenue is $ 80 \times P $.
3. The total costs are $ 1840 $ (weekly expenses).

At break-even, revenue equals expenses:

\[
80 \times P = 1840
\]

Solving for $ P $:

\[
P = \frac{1840}{80} = 23
\]

Thus, **Quickprint must charge $23 per job to break even**.

---

### (b) Price for Desired Profit

If Quickprint wishes to make a profit of **$1200**, the revenue needs to cover both the expenses and the desired profit.

1. Let $ P $ be the price per job.
2. The revenue from selling 80 jobs is $ 80 \times P $.
3. The total amount to cover is $ 1840 + 1200 = 3040 $.

So the equation becomes:

\[
80 \times P = 3040
\]

Solving for $ P $:

\[
P = \frac{3040}{80} = 38
\]

Thus, **to make a profit of $1200, Quickprint must charge $38 per job**.

---

### (c) Profit from 90 Jobs at Price in (b)

From part (b), the price per job is **$38**. Now, if Quickprint sells **90 jobs** at this price, we can calculate the profit.

1. Revenue from selling 90 jobs is $ 90 \times 38 = 3420 $.
2. The total expenses remain $1840.

The profit is:

\[
\text{Profit} = 3420 - 1840 = 1580
\]

Thus, **the profit realized from selling 90 jobs at $38 each is $1580**.

---

### (d) Minimum Price to Break Even for 100 Jobs

Now, Quickprint sells **100 jobs** and we need to determine the minimum price per job to break even.

1. Let $ P $ be the minimum price per job.
2. The revenue from 100 jobs is $ 100 \times P $.
3. To break even, revenue must equal the expenses of **$1840**.

The equation is:

\[
100 \times P = 1840
\]

Solving for $ P $:

\[
P = \frac{1840}{100} = 18.40
\]

Thus, **the minimum price to break even when selling 100 jobs is $18.40 per job**.

---

### Summary of Answers:
(a) The break-even price per job is **$23**.

(b) To make a profit of **$1200**, the price per job should be **$38**.

(c) If Quickprint sells **90 jobs at $38 each**, the profit will be **$1580**.

(d) If Quickprint sells **100 jobs**, the minimum price to break even is **$18.40**.

---

Would you like further details or clarifications? 

Here are five questions related to this problem:

1. What factors can affect the break-even price in real business scenarios?
2. How does changing the number of jobs sold impact the break-even analysis?
3. What would happen to profits if costs per job increase but the price remains fixed?
4. How can Quickprint optimize its pricing strategy to maximize profit?
5. What is the effect of fixed costs versus variable costs in this situation?

**Tip**: Understanding the relationship between fixed costs and variable costs helps in better pricing decisions, especially in varying sales volumes.

Quickprint Services operates several franchise where it prints brochures, business cards, and stationery. It plans to sell 80 jobs next week, at an average cost of $52 each. Its weekly expenses are $1840. a. How much must Quickprint charge for each job to break even? b. If it wishes to make a profit of $1200, what price does it have to charge? c. If it sells 90 jobs at the price determined in part (b), how much profit will be realized? d. If Quickprint sells 100 jobs through a special promotion, what is the minimum price it could charge to break even?

Explore how to calculate the break-even price, determine pricing for desired profit, and assess the profit when selling different quantities for Quickprint Services. This problem covers key concepts in algebra, including break-even analysis and profit calculation, suitable for students in Grades 9-12.

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