The equation for the total revenue earned by a company for selling widgets is p=4q. The equation for the total cost of the company for producing widgets if p=q+6.
Find the break-even quantity.
4q=q+6
q=2
To find the break-even quantity, we need to determine the quantity at which the total revenue is equal to the total cost. In other words, we are looking for the point where the revenue earned by selling widgets is equal to the cost of producing widgets.
The equation for total revenue (TR) is given as p = 4q, where p represents the price of a widget and q represents the quantity of widgets sold.
The equation for total cost (TC) is given as p = q + 6.
To find the break-even quantity, we need to set the total revenue equal to the total cost and solve for q.
Setting the total revenue equal to the total cost, we have:
4q = q + 6
To solve for q, we can subtract q from both sides of the equation:
4q - q = q - q + 6
3q = 6
Next, we divide both sides of the equation by 3 to isolate q:
(3q)/3 = 6/3
q = 2
Therefore, the break-even quantity, or the quantity at which the total revenue is equal to the total cost, is 2 widgets.