SUMMARY
The discussion focuses on determining the optimal number of units, t, to produce in order to achieve profit based on the cost function C = 3t² + 9t and the revenue function R = 4t² + t. To generate profit, the condition R > C must be satisfied, leading to the inequality 4t² + t > 3t² + 9t. Simplifying this results in the equation t² - 8t = 0, which identifies the break-even point for profit. The solutions indicate that t must be greater than 8 to ensure profitability.
PREREQUISITES
- Understanding of quadratic equations
- Knowledge of profit and loss concepts in economics
- Familiarity with algebraic manipulation
- Basic understanding of functions and graphs
NEXT STEPS
- Study quadratic inequalities and their graphical representations
- Learn about cost-revenue analysis in business economics
- Explore the implications of break-even analysis in production
- Investigate optimization techniques in calculus
USEFUL FOR
Students in economics, business analysts, and anyone involved in production planning and financial forecasting will benefit from this discussion.