We did not find results for: suppose a company manufactures MP3 players and sell them to retailers for $98 each. it has a fixed cost of $262,500 related to the production of the MP3 players and the cost per unit is $23 what is the total revenue function, marginal revenue for this product, total cost for this product, what is the profit function, what is the marginal profit, what is the cost revenue and profit if 0 units are produced..
Well if 0 units are produced, your profit is a loss of 262,500 which is primarily your fixed cost.
Total revenue function is 98x. X is the number of units sold.
I think marginal revenue is just revenues minus variable cost so 98x-23y would be marginal revenue. I might be wrong so double check with someone else.
Total cost for the product is 23y + 262,500.
The total profit function is 98x-23x-262,500. X is units sold. They may want you to express x as y though so it might be 98x-23y-262,500.
Let me know if this helps. Good luck
To calculate the total revenue function, we can multiply the number of units sold by the selling price per unit. Let's denote the number of units sold as q and the selling price per unit as P.
Total Revenue (TR) = q * P
Given that the selling price per unit is $98, the total revenue function is:
TR = 98q
To find the marginal revenue for this product, we need to find the derivative of the total revenue function with respect to the number of units sold (q). For a linear function such as this, the marginal revenue is constant, as it does not change with quantity. Therefore, the marginal revenue for this product is $98 per unit.
The total cost for this product can be calculated by adding the fixed cost and the variable cost. The variable cost is equal to the cost per unit multiplied by the number of units produced (q).
Fixed cost = $262,500
Variable cost per unit = $23
Total Cost (TC) = Fixed Cost + Variable Cost
TC = $262,500 + ($23 * q)
To calculate the profit function, we subtract the total cost from the total revenue.
Profit (π) = TR - TC
π = 98q - (262,500 + 23q)
The marginal profit can be found by taking the derivative of the profit function with respect to the number of units sold (q). For a linear function like this, the marginal profit is constant and equal to the marginal revenue.
Marginal Profit = Marginal Revenue = $98 per unit
Finally, if 0 units are produced (q=0), the cost, revenue, and profit can be calculated as follows:
Total Cost (TC) = $262,500 + ($23 * 0) = $262,500
Total Revenue (TR) = 98 * 0 = $0
Profit (π) = TR - TC = $0 - $262,500 = -$262,500
Therefore, if 0 units are produced, the cost is $262,500, the revenue is $0, and the profit is -$262,500.
To find the total revenue function, we need to multiply the selling price of each unit by the number of units sold. The selling price is given as $98 per unit.
So, the total revenue function (R) is given by:
R = Selling Price per unit * Number of units sold
Since the number of units sold can vary, we can represent it as 'x'. Therefore, the total revenue function becomes:
R(x) = 98x
To find the marginal revenue for this product, we need to determine the rate at which the revenue is changing with respect to the number of units sold. The marginal revenue is calculated as the derivative of the total revenue function.
In this case, the marginal revenue (MR) would be:
MR(x) = dR/dx
To calculate the total cost for this product, we need to consider both fixed costs and variable costs. The fixed cost related to the production of the MP3 players is given as $262,500. This cost remains constant regardless of the number of units produced. The variable cost per unit is $23.
So, the total cost function (C) is given by:
C(x) = Fixed Cost + Variable Cost per unit * Number of units (x)
Substituting the given values, the cost function becomes:
C(x) = 262,500 + 23x
To calculate the profit function, we subtract the total cost from the total revenue. Therefore, the profit function (P) is given by:
P(x) = R(x) - C(x)
Substituting the respective revenue and cost functions, the profit function becomes:
P(x) = 98x - (262,500 + 23x)
The marginal profit can be found by taking the derivative of the profit function. Therefore, the marginal profit (MP) is given by:
MP(x) = dP/dx
Now, if 0 units are produced, we can substitute x=0 into the revenue, cost, and profit functions to determine their respective values.
For revenue (R):
R(0) = 98 * 0 = 0
For cost (C):
C(0) = 262,500 + 23 * 0 = 262,500
For profit (P):
P(0) = 98 * 0 - (262,500 + 23 * 0) = -262,500
So, if 0 units are produced, the revenue is 0, the cost is $262,500, and the profit is -$262,500.