Math Problem Statement
A fast-food restaurant has a cost of production C(x) = 7x + 140 and a revenue function R(x) = 11x. When does the company start to turn a profit?
Solution
The problem asks when the company starts to turn a profit, given:
- Cost function:
- Revenue function:
To determine when the company starts turning a profit, we need to find when the revenue is greater than the cost. This happens when:
Substituting the given functions:
Now, solve this inequality:
So, the company will start turning a profit when the production level is at least 36 units (since it must be greater than 35).
Let me know if you'd like more details or have any questions!
Here are five related questions:
- How does increasing the revenue per unit affect the break-even point?
- What if the fixed cost (currently 140) increases—how does that impact profit?
- Can you determine the break-even point by equating the cost and revenue functions?
- How would the profit function look in this case?
- What happens to the profit if the variable cost per unit changes?
Tip: Always check for break-even by setting revenue equal to cost, then find the point when revenue exceeds cost for profitability!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Functions
Inequalities
Formulas
C(x) = 7x + 140
R(x) = 11x
Theorems
Solving linear inequalities
Suitable Grade Level
Grades 9-12