Math Problem Statement

The figure shows graphs of the total costs and the total revenue functions for a commodity. (Assume cost and revenue are measured in dollars.) R-C Match the question with the correct answer.

Determine the fixed cost. a. Total revenue function

Determine the dollars for break-even. b. 40 units

Estimate the marginal revenue. c. 7.5

Label function B d. 2.5

Label function A e. $300

Estimate the marginal cost. f. Total cost function

Determine the number of units to break-even. g. $200

Solution

To match the question with the correct answer based on the provided context, here's the appropriate pairing:

  1. Determine the fixed cost.
    g. $200
    (Fixed cost is typically the y-intercept of the total cost function, indicating the cost when no units are produced.)

  2. Determine the dollars for break-even.
    e. $300
    (This refers to the revenue level where the company breaks even—i.e., when total cost equals total revenue.)

  3. Estimate the marginal revenue.
    c. 7.5
    (Marginal revenue refers to the increase in revenue for each additional unit sold.)

  4. Label function B.
    a. Total revenue function
    (Function B is the total revenue curve.)

  5. Label function A.
    f. Total cost function
    (Function A represents the total cost curve.)

  6. Estimate the marginal cost.
    d. 2.5
    (Marginal cost is the increase in cost for each additional unit produced.)

  7. Determine the number of units to break-even.
    b. 40 units
    (This is the quantity where total cost equals total revenue, leading to no profit or loss.)


Do you want details on any specific answers or have any other questions?

Five related questions:

  1. How do you calculate the marginal cost from a graph?
  2. What is the significance of the break-even point in business?
  3. How can fixed costs affect the profitability of a company?
  4. What is the relationship between marginal cost and marginal revenue in profit maximization?
  5. How do total revenue and total cost curves help in decision-making for businesses?

Tip:

In economics, the break-even point occurs when total revenue equals total costs, resulting in zero profit or loss, a crucial concept for determining a company's financial viability.

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Math Problem Analysis

Mathematical Concepts

Cost Analysis
Revenue Analysis
Break-even Point
Marginal Cost
Marginal Revenue

Formulas

Break-even Point: Total Revenue = Total Cost
Marginal Cost: MC = ΔTotal Cost / ΔQuantity
Marginal Revenue: MR = ΔTotal Revenue / ΔQuantity

Theorems

Break-even Analysis
Marginal Cost and Revenue

Suitable Grade Level

Grades 10-12