Let's work through each part of the problem step by step.

1. Revenue Function:

The revenue function $R(x)$ represents the total money earned from selling $x$ items. Since each TV is sold for $372, the revenue function is:

$R(x) = 372x$

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2. Profit Function:

The profit function $P(x)$ is given by the difference between revenue and cost, i.e.,

$P(x) = R(x) - C(x)$

Substitute $R(x) = 372x$ and $C(x) = 72x + 3600$ into the equation:

$P(x) = 372x - (72x + 3600)$

Simplify the equation:

$P(x) = 372x - 72x - 3600$ $P(x) = 300x - 3600$

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3. Revenue from Selling 336 Items:

To find the revenue from selling 336 items, substitute $x = 336$ into the revenue function:

$R(336) = 372 \times 336$

Calculating:

$R(336) = 125,092$

So, the revenue from selling 336 items is $125,092.

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4. Cost of Producing 336 Items:

To find the cost of producing 336 items, substitute $x = 336$ into the cost function:

$C(336) = 72 \times 336 + 3600$

Calculating:

$C(336) = 24,192 + 3600 = 27,792$

So, the cost of producing 336 items is $27,792.

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5. Profit on 336 Items:

To find the profit from selling 336 items, substitute $x = 336$ into the profit function:

$P(336) = 300 \times 336 - 3600$

Calculating:

$P(336) = 100,800 - 3600 = 97,200$

So, the profit from selling 336 items is $97,200.

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Summary of Results:

1. Revenue function: $R(x) = 372x$
2. Profit function: $P(x) = 300x - 3600$
3. Revenue from selling 336 items: $125,092
4. Cost of producing 336 items: $27,792
5. Profit on 336 items: $97,200

Would you like more details or have any questions?

Here are five related questions:

1. What would the profit be if the manufacturer produced 500 items?
2. How would the profit change if the price per TV were increased to $400?
3. What is the break-even point (number of items sold where profit is zero)?
4. How does a change in fixed costs affect the profit function?
5. What is the marginal revenue for each additional TV sold?

Tip: When calculating profit, always consider both fixed and variable costs. This helps in understanding how scaling production affects profitability.