High School Calculus Discussion

The goal is to optimize income for the transportation systemI am doing a math project and need help incorporating the equations of marginal revenue, marginal cost, and the function of derivatives to answer my question. we wanted to determine the maximum profit a mts can make by figuring out what numbers to use for the equations and solve them.This is the report we have so far for our project so we need to solve the math with an explanation and see step by step how using this math can get us an answer on what to change or how to maximize the profit for the transportation system (san diego mts).The San Diego MTS travels at 55 mph while covering 65 miles of San Diego. Its annual income rate was 360.0 million in 2021. While the day pass is $6.00 and the monthly pass is $72.00, charging citizens $0.50 per mile the ride will increase the annual income towards The San Diego MTS. According to sdmts.com, an average rider travels 15 miles a day. Draft so farTo maximize the profit from public transportation systems the concept of marginal revenue and marginal cost can be used. By setting the marginal revenue equal to the marginal cost and then determining the level of output that corresponds to this point. Minimum and maximum derivatives can also be used to optimize systems and achieve desired outcomes as it helps identify the highest point of profit through the slope curve. To add on, using the minimum derivative optimizes public transportation systems by identifying where the point of the slope cost is at its lowest.Derivatives of a function are used to calculate speed or distance traveled, such as miles per hour and kilometers per hour. This is a measurement that is used to determine how quickly the derivative changes the value of Y with the change in the value of X. Derivatives are used every day by certain employers to help determine something changing. For example, the change of speed in trains, buses, cars, and planes is solved with calculus.The formulas we plan on using is derivative of a function:F(x) = lim (h->0) [f(x)(x+h) – f(x))/h]This formula gives the slope of the tangent line to the graph of the function f(x) at any given point x. The derivative is forming a base for a plan in calculus and is used to find the rate of change of a function. To find the marginal cost and marginal revenue, we take the derivative of the cost function and revenue function. The marginal cost is the derivative of the total cost function with respect to the quantity of output:MC(q) = dC(q)/dqMC(q) is the marginal cost, C(q) is the total cost function, and q is the quantity of output.MR(q) = dR(q)/dqMR(q) is the marginal revenue, R(q) is the total revenue function, and q is the quantity of output.