A videocassette manufacturer has determined that its weekly cost equation is C = 3000 + 10x, where x is the number of cassettes produced and sold each week. If cassettes are sold for $15 each to distributions, how many must be sold each week for the company to make a profit?
To determine the number of cassettes that need to be sold each week for the company to make a profit, we need to set up a profit equation.
The profit equation is given by: Profit = Revenue - Cost.
The revenue from selling the cassettes can be calculated by multiplying the selling price per cassette ($15) by the number of cassettes sold (x). Therefore, the revenue can be expressed as: Revenue = 15x.
The cost equation is given as: C = 3000 + 10x.
Substituting the revenue and cost equations into the profit equation, we get:
Profit = 15x - (3000 + 10x).
To determine the breakeven point where the profit is zero, we set the profit equation equal to zero:
0 = 15x - (3000 + 10x).
Simplifying the equation, we get:
0 = 15x - 3000 - 10x.
Combining like terms, we get:
0 = 5x - 3000.
Adding 3000 to both sides, we get:
5x = 3000.
Dividing both sides by 5, we find:
x = 600.
Therefore, the company must sell at least 600 cassettes each week to make a profit.