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A manufacturer of DVD players has weekly fixed costs of $1,520 and variable costs of $12.50 per units for one particular model. The company sells this model to dealers for $19.50 each.Match the statement with the correct answer.Write the function for the weekly total costs, C(x). Write the function for the total revenue function, R(x). Write the function for the profit function, P(x). This is the cost (in dollars) of producing 150 DVD players. This is the profit (in dollars) when 150 DVD players are sold but since it is negative it means that the company loses money when 150 DVD players are sold. Each additional DVD player sold increases the profit by this many dollars. This is the revenue (in dollars) generated from the sale of 150 DVD players.

Question

A manufacturer of DVD players has weekly fixed costs of 1,520andvariablecostsof1,520 and variable costs of 12.50 per units for one particular model. The company sells this model to dealers for $19.50 each.Match the statement with the correct answer.Write the function for the weekly total costs, C(x). Write the function for the total revenue function, R(x). Write the function for the profit function, P(x). This is the cost (in dollars) of producing 150 DVD players. This is the profit (in dollars) when 150 DVD players are sold but since it is negative it means that the company loses money when 150 DVD players are sold. Each additional DVD player sold increases the profit by this many dollars. This is the revenue (in dollars) generated from the sale of 150 DVD players.

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Solution

  1. The function for the weekly total costs, C(x), is C(x) = 1520 + 12.50x. This is because the fixed costs are 1520andthevariablecostsare1520 and the variable costs are 12.50 per unit.

  2. The function for the total revenue function, R(x), is R(x) = 19.50x. This is because each DVD player is sold for $19.50.

  3. The function for the profit function, P(x), is P(x) = R(x) - C(x) = 19.50x - (1520 + 12.50x) = 7x - 1520. This is the revenue minus the cost.

  4. The cost (in dollars) of producing 150 DVD players is C(150) = 1520 + 12.50*150 = $3370.

  5. The profit (in dollars) when 150 DVD players are sold is P(150) = 7*150 - 1520 = -$20. Since this is negative, it means that the company loses money when 150 DVD players are sold.

  6. Each additional DVD player sold increases the profit by $7. This is the coefficient of x in the profit function.

  7. The revenue (in dollars) generated from the sale of 150 DVD players is R(150) = 19.50*150 = $2925.

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