income = 115 n
cost = 8600 + 55 n
so
profit = 115 n - 8600 - 55 n
= 60 n - 8600
That means we do not start making money until we sell 8600/60 = 143 1/3 of the players. After that we will make 60 dollars per unit.
cost = 8600 + 55 n
so
profit = 115 n - 8600 - 55 n
= 60 n - 8600
That means we do not start making money until we sell 8600/60 = 143 1/3 of the players. After that we will make 60 dollars per unit.
Total Cost:
The total cost consists of fixed costs and variable costs.
Fixed Costs: The fixed costs for this CD player model are given as $8600 per month. Since fixed costs remain constant regardless of the number of units produced or sold, the fixed cost can be considered as a constant value.
Variable Costs: The variable cost per unit is given as $55. This means that for every unit produced, the cost of producing it is $55.
Total Revenue:
The total revenue is obtained by multiplying the selling price per unit by the number of units sold.
Selling Price per Unit: The selling price to dealers for each unit is given as $115.
Now we can use this information to find the profit function. Let's define 'x' as the number of units produced/sold.
Total Cost Function:
The total cost function (TC) can be calculated by adding the fixed costs and the variable costs.
TC = Fixed Costs + (Variable Cost per Unit * Number of Units)
TC = 8600 + (55 * x)
Total Revenue Function:
The total revenue function (TR) can be calculated by multiplying the selling price per unit by the number of units sold.
TR = Selling Price per Unit * Number of Units
TR = 115x
Profit Function:
The profit function (P) can be calculated by subtracting the total cost from the total revenue.
P = TR - TC
P = (115x) - (8600 + 55x)
Simplifying the equation further:
P = 115x - 8600 - 55x
P = 60x - 8600
Therefore, the profit function for the CD player manufacturer is P(x) = 60x - 8600, where x represents the number of units produced/sold.