Annual profit in thousands of dollars is given by the function, P(x) = -.1x2 + 50x - 300, where x is the number of items sold, x ¡Ý 0.
describe the meaning of the number -.1 in the formula
describe the meaning of the number -300 in the formula
- 300 represents the fixed cost which rmains the same regardless of x
In the given function, P(x) = -.1x^2 + 50x - 300, the coefficients in the formula have specific meanings:
1. The number -.1:
In this formula, the number -.1 is the coefficient of the x^2 term, which is multiplied by the square of the number of items sold. A negative value for this coefficient indicates that the profit function is a downward-opening parabola. The value of -.1 means that for each additional item sold, the profit decreases by 0.1 thousand dollars. It represents the rate of change of profit with respect to the number of items sold, suggesting that as more items are sold, the rate at which profit decreases becomes steeper.
2. The number -300:
In this formula, the number -300 is the constant term, which does not depend on the number of items sold. It represents a fixed cost or expense that the business incurs regardless of the number of items sold. A negative value for this constant term indicates that it is subtracted from the profit. This constant cost of -300 represents the initial investment, expenditures, or overhead expenses that need to be covered before any profit can be realized. It affects the overall profit level, as it reduces the profit by 300 thousand dollars regardless of the sales volume.
Overall, the coefficient -.1 and the constant term -300 in the formula have different meanings in the context of the profit function. The coefficient -.1 affects the rate at which profit changes with respect to the number of items sold, while the constant term -300 represents a fixed cost or expense that is subtracted from the profit.