Marginal Cost = 30sqroot(x+4) with fixed costs of $1000.
Marginal Revenue = 900.
find profit or loss from production and sale of 5 units.
how many units will result in a max profit?
what is the max profit?
Can someone please help. Trying to review for my final and really stuck!
Nuts to the problem. How can marginal cost have fixed costs?
Secondly, fixed costs should be when x=0. The marginal cost with x=0 is 60. This is an odd problem.
To calculate the profit or loss from the production and sale of 5 units, we need to find the total cost and total revenue.
The total cost is the sum of the fixed costs and the variable costs. In this case, the fixed cost is given as $1000. The variable cost is determined by the marginal cost function.
To calculate the variable cost for 5 units, we substitute x = 5 into the marginal cost function:
Marginal Cost = 30√(x+4)
Marginal Cost = 30√(5+4)
Marginal Cost = 30√9
Marginal Cost = 30 * 3
Marginal Cost = $90
So the variable cost for producing 5 units is $90.
Now, let's calculate the total cost:
Total Cost = Fixed Cost + Variable Cost
Total Cost = $1000 + $90
Total Cost = $1090
The total revenue is given by the marginal revenue function, which is $900.
Now we can calculate the profit or loss:
Profit = Total Revenue - Total Cost
Profit = $900 - $1090
Profit = -$190
Therefore, the production and sale of 5 units would result in a loss of $190.
To determine the number of units that result in maximum profit, we need to find the point of maximum profit on the profit function.
The profit function is given by:
Profit = (Marginal Revenue - Marginal Cost) * x - Fixed Cost
To find the maximum profit, we can take the derivative of the profit function with respect to x and set it equal to zero.
Now, let's differentiate the profit function:
dProfit/dx = (d(Marginal Revenue)/dx - d(Marginal Cost)/dx) * x + (Marginal Revenue - Marginal Cost)
Setting the derivative equal to zero:
0 = (d(Marginal Revenue)/dx - d(Marginal Cost)/dx) * x + (Marginal Revenue - Marginal Cost)
Solve for x using the marginal revenue and marginal cost functions:
0 = (0 - 30/2√(x+4)) * x + 900 - 30√(x+4)
Simplifying the equation:
0 = -15x/√(x+4) + 900 - 30√(x+4)
To solve this equation for x, you can use numerical methods or approximation techniques such as guess-and-check, graphing the two functions, or using a calculator or software.
Once you find the value of x that maximizes profit, substitute it into the profit function to find the maximum profit.
Unfortunately, it seems that there might be an error or inconsistency in the given information or problem statement. The concept of marginal cost typically refers to the additional cost of producing one additional unit, and it is usually a function of the quantity produced. Fixed costs, on the other hand, are costs that do not change with the quantity produced. It is unusual for the marginal cost function to include fixed costs.
I would recommend double-checking the problem statement or referring to additional resources or examples for clarification.