A company produces two products, A and B. The production cost for product A is modeled by A(x)=5x+100A(x)=5x+100, and for product B, it is modeled by B(x)=3x+50B(x)=3x+50, where xx is the number of units produced. What function represents the difference in production costs between the two products?

Question 41Answer

D(x)=2x+150D(x)=2x+150

D(x)=2x+50D(x)=2x+50

D(x)=8x+150D(x)=8x+150

D(x)=8x+50

To find the function that represents the difference in production costs between products A and B, we start by analyzing the given cost functions:

- The production cost for product A is given by:  
  \( A(x) = 5x + 100 \)  
  where \( x \) is the number of units produced.
  
- The production cost for product B is given by:  
  \( B(x) = 3x + 50 \).  

The difference in production costs between the two products can be represented by subtracting the cost function of product B from the cost function of product A:

\[
D(x) = A(x) - B(x)
\]

Substituting the given functions:

\[
D(x) = (5x + 100) - (3x + 50)
\]

Simplify the expression:

\[
D(x) = 5x + 100 - 3x - 50
\]

\[
D(x) = (5x - 3x) + (100 - 50)
\]

\[
D(x) = 2x + 50
\]

So, the function that represents the difference in production costs between the two products is:

\[
\boxed{D(x) = 2x + 50}
\]

Therefore, the correct answer is:

**D(x) = 2x + 50**

Do you want more details or have any questions?

Here are 5 related questions:

1. How would the difference in costs change if the coefficients of \( x \) in both functions were doubled?
2. What happens to the difference in production costs if the fixed costs of both products are the same?
3. How would the function change if a third product C with a different cost function was introduced?
4. What is the significance of the slope in the difference function \( D(x) \)?
5. How would you determine the break-even point for the difference in costs between the two products?

**Tip:** Always ensure to simplify expressions correctly by carefully handling signs and coefficients during subtraction or addition of functions.

A company produces two products, A and B. The production cost for product A is modeled by A(x)=5x+100, and for product B, it is modeled by B(x)=3x+50, where x is the number of units produced. What function represents the difference in production costs between the two products?

Learn how to calculate the difference in production costs between two products using linear functions. This problem involves algebraic concepts and the formula for the difference of two linear cost functions, suitable for students in Grades 8-10.

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