please show all steps and formulas used, thank you, and if possible please don't write in cursive

MTH 1120 (03) Mathematical Analysis II Winter 2023 Homework 7 1. The total cost C (in dollars) of operating a factory is C = 0.5362 +10x + 7200, where x is the number of units produced. At what level of production will the average cost per unit be minimized? (The average cost per unit is Clx.) 2. Find the point of diminishing returns for the function, where R is the revenue (in thousands of dollars) and x is the advertising cost (in thousands of dollars). Rzgx3+4x3+12, 05x55 3. Determine the price that will maximize profit for the demand and cost functions, where p is the price, x is the number of units, and C is the cost. Demand Function Cost Function 24 p= C=O.4x+600 J} 4. A rectangular solid with a square base has a surface area of 432 square centimeters. a) Determine the dimensions that yield the maximum volume. b) Find the maximum volume. 5. Find the number of units 3: that maximizes the revenue, R = 363'2 0.053(3