Let's break down the components to match each part of the problem with the correct answer. We'll define the functions and evaluate them based on the given information.

Given:

• Fixed costs (weekly): $1,520
• Variable costs per unit: $12.50
• Selling price per unit: $19.50

1. Write the function for the weekly total costs, $C(x)$:

The total cost function includes both fixed costs and variable costs. The formula is: $C(x) = \text{Fixed costs} + (\text{Variable cost per unit} \times \text{Number of units})$ $C(x) = 1,520 + 12.50x$ So, the total cost function is: $C(x) = 1,520 + 12.50x$

2. Write the function for the total revenue function, $R(x)$:

Revenue is calculated by multiplying the number of units sold by the selling price per unit. The formula is: $R(x) = \text{Selling price per unit} \times \text{Number of units}$ $R(x) = 19.50x$ So, the total revenue function is: $R(x) = 19.50x$

3. Write the function for the profit function, $P(x)$:

Profit is calculated as total revenue minus total costs. The formula is: $P(x) = R(x) - C(x)$ $P(x) = 19.50x - (1,520 + 12.50x)$ Simplifying: $P(x) = 19.50x - 1,520 - 12.50x$ $P(x) = 7x - 1,520$ So, the profit function is: $P(x) = 7x - 1,520$

4. The cost (in dollars) of producing 150 DVD players:

To find the cost for producing 150 DVD players, substitute $x = 150$ into the cost function $C(x)$: $C(150) = 1,520 + 12.50(150)$ $C(150) = 1,520 + 1,875 = 3,395$ So, the cost of producing 150 DVD players is $3,395.

5. The profit (in dollars) when 150 DVD players are sold:

To find the profit when 150 DVD players are sold, substitute $x = 150$ into the profit function $P(x)$: $P(150) = 7(150) - 1,520$ $P(150) = 1,050 - 1,520 = -470$ So, the company loses $470 when selling 150 DVD players.

6. Each additional DVD player sold increases the profit by this many dollars:

The profit per additional DVD player is the coefficient of $x$ in the profit function $P(x) = 7x - 1,520$, which is $7.

7. The revenue (in dollars) generated from the sale of 150 DVD players:

To find the revenue when 150 DVD players are sold, substitute $x = 150$ into the revenue function $R(x)$: $R(150) = 19.50(150)$ $R(150) = 2,925$ So, the revenue generated from selling 150 DVD players is $2,925.

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Summary:

1. The total cost function: $C(x) = 1,520 + 12.50x$
2. The total revenue function: $R(x) = 19.50x$
3. The profit function: $P(x) = 7x - 1,520$
4. The cost of producing 150 DVD players: $3,395
5. The profit (or loss) when 150 DVD players are sold: -$470 (loss)
6. Each additional DVD player sold increases the profit by: $7
7. The revenue generated from selling 150 DVD players: $2,925

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Do you need further details or have any questions?
Here are 5 related questions to expand this concept:

1. How many DVD players must the company sell to break even?
2. What is the company's profit if they sell 500 DVD players in a week?
3. How would a change in the fixed costs affect the break-even point?
4. What is the marginal cost of producing each additional DVD player?
5. If the selling price is increased to $22.50, what happens to the profit function?

Tip: In cost-profit analysis, understanding the break-even point helps determine when revenue covers all costs, resulting in zero profit or loss.