Final answer:
The correct equation to represent the company's weekly profit in thousands of dollars, y, when x items are sold is B. y = -x² + 50x - 300.The correct answer is option b.
Step-by-step explanation:
The question deals with finding an equation that represents the weekly profit (in thousands of dollars, y), as a function of the number of items sold (x). Among the given options, we are looking for an equation that is not linear, as the profit is not likely to change at a constant rate with the number of items sold.
Typically, profit might initially rise with sales but could level off or decrease due to various factors such as production costs and market saturation. Therefore, we can eliminate linear equations such as those given in the examples that have the form y = mx + b, where m is the slope and b is the y-intercept.
Given this, we can focus on the nonlinear equations in the question, which are quadratic, and represent more complex relationships between number of items sold and profit.
By examining these, we can conclude that the correct option is B. y = -x² + 50x - 300. This quadratic equation suggests that there is a peak profit that the company can make before the profit starts to decrease, perhaps due to the increasing costs of producing a larger number of items.