Question

Suppose a company has fixed costs of $300 and variable cost per unit of3/4x +1460 dollars, where x is the total number of units produced. Suppose further that the selling price of its product is 1500− 1/4x dollars per unit.

a. Find the break-even points.
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Answer 1

To find the break-even points, set total revenue equal to total cost and solve the resulting quadratic equation for x. These points occur where the firm's revenue and costs are equal, indicating no profit or loss.

Step-by-step explanation:

To find the break-even points, we need to set the total revenue equal to the total cost. The total cost (TC) is the sum of fixed costs and variable costs, given by TC = 300 + (3/4)x + 1460. The total revenue (TR) is the number of units sold times the selling price per unit, given by TR = x(1500 - 1/4x).

To find the break-even points, we equate TR and TC and solve for x:

1. Set TR = TC: x(1500 - 1/4x) = 300 + (3/4)x + 1460.
2. Simplify and solve for x: 1500x - (1/4)x^2 = (3/4)x + 1760.
3. Bring all terms to one side: (1/4)x^2 + (1/2)x - 1500x + 1760 = 0.
4. Solve the quadratic equation for x to find the break-even quantities.

Note that break-even points occur where the firm's total revenues are equal to its total costs, resulting in no profit or loss.