Answer :
Final answer:
The cost function is C(x) = $29,000 + ($8 * x). The revenue function is R(x) = $11 * x. The profit function is P(x) = ($11 * x) - ($29,000 + ($8 * x)). The profit (loss) corresponding to the production levels P(6,200), P(7,900), and P(12,200) can be calculated by substituting the production levels into the profit function and evaluating the expression.
Explanation:
To find the cost function, we need to consider the fixed cost and the variable cost per unit. The fixed cost is given as $29,000, which means it remains constant regardless of the number of units produced. The variable cost per unit is $8.
The cost function, denoted as C(x), represents the total cost incurred by the company to produce x units. It can be calculated by adding the fixed cost to the product of the variable cost per unit and the number of units produced:
C(x) = Fixed Cost + (Variable Cost per Unit * Number of Units)
Substituting the given values:
C(x) = $29,000 + ($8 * x)
To find the revenue function, we need to consider the selling price per unit. The selling price per unit is $11.
The revenue function, denoted as R(x), represents the total revenue generated by selling x units. It can be calculated by multiplying the selling price per unit by the number of units sold:
R(x) = Selling Price per Unit * Number of Units
Substituting the given value:
R(x) = $11 * x
To find the profit function, we subtract the cost function from the revenue function:
P(x) = R(x) - C(x)
Substituting the previously calculated functions:
P(x) = ($11 * x) - ($29,000 + ($8 * x))
To compute the profit (loss) at specific production levels, we substitute the production levels into the profit function and evaluate the expression:
P(6,200) = ($11 * 6,200) - ($29,000 + ($8 * 6,200))
P(7,900) = ($11 * 7,900) - ($29,000 + ($8 * 7,900))
P(12,200) = ($11 * 12,200) - ($29,000 + ($8 * 12,200))
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Final answer:
The cost function is C(x) = $29,000 + ($8 * x). The revenue function is R(x) = $11 * x. The profit function is P(x) = ($11 * x) - ($29,000 + ($8 * x)). The profit (loss) corresponding to the production levels P(6,200), P(7,900), and P(12,200) can be calculated by substituting the production levels into the profit function and evaluating the expression.
Explanation:
To find the cost function, we need to consider the fixed cost and the variable cost per unit. The fixed cost is given as $29,000, which means it remains constant regardless of the number of units produced. The variable cost per unit is $8.
The cost function, denoted as C(x), represents the total cost incurred by the company to produce x units. It can be calculated by adding the fixed cost to the product of the variable cost per unit and the number of units produced:
C(x) = Fixed Cost + (Variable Cost per Unit * Number of Units)
Substituting the given values:
C(x) = $29,000 + ($8 * x)
To find the revenue function, we need to consider the selling price per unit. The selling price per unit is $11.
The revenue function, denoted as R(x), represents the total revenue generated by selling x units. It can be calculated by multiplying the selling price per unit by the number of units sold:
R(x) = Selling Price per Unit * Number of Units
Substituting the given value:
R(x) = $11 * x
To find the profit function, we subtract the cost function from the revenue function:
P(x) = R(x) - C(x)
Substituting the previously calculated functions:
P(x) = ($11 * x) - ($29,000 + ($8 * x))
To compute the profit (loss) at specific production levels, we substitute the production levels into the profit function and evaluate the expression:
P(6,200) = ($11 * 6,200) - ($29,000 + ($8 * 6,200))
P(7,900) = ($11 * 7,900) - ($29,000 + ($8 * 7,900))
P(12,200) = ($11 * 12,200) - ($29,000 + ($8 * 12,200))
Learn more about cost, revenue, and profit functions here:
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