Solve Problems Using Systems of Linear Equations
-How many binoculars must be produced and sold for the company to break even?
A) 750 binoculars
B) 2250 binoculars
C) 1500 binoculars
D) 2700 binoculars

Question

Quizplus · Accepted Answer

The company breaks even when the total revenue equals the total cost. The total revenue is the number of binoculars sold multiplied by the price per binocular. The total cost is the fixed cost plus the variable cost per binocular multiplied by the number of binoculars sold. The break-even point is the number of binoculars sold when the total revenue equals the total cost.In this case, the fixed cost is $1,000,000, the variable cost per binocular is $200, and the price per binocular is $300. The total revenue is 300x, where x is the number of binoculars sold. The total cost is 1,000,000 + 200x. The break-even point is when 300x = 1,000,000 + 200x. Solving for x, we get x = 750.Therefore, the company must produce and sell 750 binoculars to break even.