Final answer:
The function represents the cost structure of Glorious Gadgets involving a variable cost, an inverse relation cost component, and a fixed cost. It's a mathematical model used to calculate the total cost based on the number of astronomy equipment units sold.
Step-by-step explanation:
The question concerns the function C(x)=3.5x+47250x^(-1)+13500 which models the cost structure of a company named Glorious Gadgets.
This function likely represents the total cost to the company when purchasing and selling x amount of astronomy equipment. It is composed of three terms. The first term, 3.5x, could represent the variable cost per unit of product. The second term, 47250x^(-1) or 47250/x, appears to represent costs that are inversely related to the number of units (possibly fixed costs spread over more units reduce the cost per unit). The third term, 13500, is likely a fixed cost that doesn't change with the number of units sold.
To analyze this cost function further, we might want to calculate its derivative to find the marginal cost, or how cost changes with each additional unit produced. This could involve applying the power rule and the constant multiple rule for derivatives.