Final answer:
The question involves using algebra and graphing to solve for the equilibrium price and quantity of cellphones produced and sold by a company, based on the provided weekly price-demand and cost equations.
Step-by-step explanation:
The question provided pertains to the application of algebra and graphing techniques to solve a business problem involving the manufacturing and selling of cell phones. Specifically, it asks for an understanding of the company's weekly price demand and cost equations. The price-demand equation is represented as P = 600 - 0.1x, indicating that the price that consumers are willing to pay decreases as the quantity of cellphones, x, increases. The cost equation C(x) = 20,000 + 130x shows the total cost of producing x cellphones, including both fixed and variable costs.
To find the equilibrium price and quantity, we can set the demand equal to the supply, and graphically, this is represented by the point where the demand curve intersects with the cost or supply curve. This approach allows us to visualize how varying the number of cellphones (x) affects the price (P), enabling us to solve for the equilibrium without relying solely on algebraic manipulation. Determining this intersection can help the company understand at what price and quantity they can maximize their profit, or in other cases, how to balance supply and demand.