Example:
On Ikea's website, the MÖRBYLÅNGA table sells for $399.00. Suppose Ikea's cost to produce 𝑡 tables is
𝐶(𝑡) = 200𝑡 + 275,000.

Please do the following problems, show your work, and then bold the correct problem:

a. If Ikea manufactures and sells zero tables, what is Ikea’s
i. revenue?
ii. cost?
iii. profit?
b. If Ikea manufactures and sells 3,500 tables, what is Ikea’s
i. revenue?
ii. cost?
iii. profit?
c. If Ikea manufactures and sells 1,250 tables, what is Ikea’s
i. revenue?
ii. cost?
iii. profit?


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

### Problem Setup
- The selling price of each table is $399.00.
- The cost function for producing $ t $ tables is given by:
  \[
  C(t) = 200t + 275,000
  \]
- The revenue function $ R(t) $ is the price per table times the number of tables sold:
  \[
  R(t) = 399t
  \]
- The profit function $ P(t) $ is the revenue minus the cost:
  \[
  P(t) = R(t) - C(t) = 399t - (200t + 275,000)
  \]

### a. If Ikea manufactures and sells zero tables:
#### i. Revenue:
\[
R(0) = 399(0) = 0
\]
**Revenue = $0**

#### ii. Cost:
\[
C(0) = 200(0) + 275,000 = 275,000
\]
**Cost = $275,000**

#### iii. Profit:
\[
P(0) = 0 - 275,000 = -275,000
\]
**Profit = -$275,000**

### b. If Ikea manufactures and sells 3,500 tables:
#### i. Revenue:
\[
R(3500) = 399(3500) = 1,396,500
\]
**Revenue = $1,396,500**

#### ii. Cost:
\[
C(3500) = 200(3500) + 275,000 = 700,000 + 275,000 = 975,000
\]
**Cost = $975,000**

#### iii. Profit:
\[
P(3500) = 1,396,500 - 975,000 = 421,500
\]
**Profit = $421,500**

### c. If Ikea manufactures and sells 1,250 tables:
#### i. Revenue:
\[
R(1250) = 399(1250) = 498,750
\]
**Revenue = $498,750**

#### ii. Cost:
\[
C(1250) = 200(1250) + 275,000 = 250,000 + 275,000 = 525,000
\]
**Cost = $525,000**

#### iii. Profit:
\[
P(1250) = 498,750 - 525,000 = -26,250
\]
**Profit = -$26,250**

---

### Summary:
- **a.** $ i. $ **Revenue = $0** $ ii. $ **Cost = $275,000** $ iii. $ **Profit = -$275,000**
- **b.** $ i. $ **Revenue = $1,396,500** $ ii. $ **Cost = $975,000** $ iii. $ **Profit = $421,500**
- **c.** $ i. $ **Revenue = $498,750** $ ii. $ **Cost = $525,000** $ iii. $ **Profit = -$26,250**

Would you like further details or have any questions?

---

### Related Questions:
1. What would the break-even point be where Ikea neither makes a profit nor incurs a loss?
2. How would the cost function change if the fixed cost increased to $300,000?
3. What would the profit be if Ikea sells 2,500 tables?
4. If Ikea reduces the price of the table to $350, how would the profit for selling 3,500 tables change?
5. How many tables must Ikea sell to make a profit of $100,000?

### Tip:
In profit calculations, understanding the fixed and variable costs can help you determine how many units you need to sell to break even or reach a target profit.

On Ikea's website, the MÖRBYLÅNGA table sells for $399.00. Suppose Ikea's cost to produce 𝑡 tables is 𝐶(𝑡) = 200𝑡 + 275,000. Please do the following problems, show your work, and then bold the correct problem: a. If Ikea manufactures and sells zero tables, what is Ikea’s i. revenue? ii. cost? iii. profit? b. If Ikea manufactures and sells 3,500 tables, what is Ikea’s i. revenue? ii. cost? iii. profit? c. If Ikea manufactures and sells 1,250 tables, what is Ikea’s i. revenue? ii. cost? iii. profit?

Explore a detailed analysis of revenue, cost, and profit for the Ikea MÖRBYLÅNGA table. This problem involves linear functions and calculations for various scenarios where different quantities of tables are sold. Ideal for students in Grades 9-11.

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