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- The O'Neill Shoe Manufacturing Company will produce a special-style shoe if the order size is large enough to provide a reasonable profit. For each special-style order, the company incurs a fixed cost of $1200 for the production setup. The variable cost is $20 per pair, and each pair sells for $30. Let x indicate the number of pairs of shoes produced. Develop a mathematical model for the total cost of producing x pairs of shoes. Express your answer in terms of x.TC = Let P indicate the total profit. Develop a mathematical model for the total profit realized from an order for x pairs of shoes. Express your answer in terms of x.P = How large must the shoe order be before O'Neill will break even? Round your answer to the nearest whole number.x = fill in the blank 3The O'Neill Shoe Manufacturing Company will produce a special-style shoe if the order size is large enough to provide a reasonable profit. For each special-style order, the company incurs a fixed cost of $1200 for the production setup. The variable cost is $20 per pair, and each pair sells for $30. Let x indicate the number of pairs of shoes produced. Develop a mathematical model for the total cost of producing x pairs of shoes. Express your answer in terms of x.TC = Let P indicate the total profit. Develop a mathematical model for the total profit realized from an order for x pairs of shoes. Express your answer in terms of x.P = How large must the shoe order be before O'Neill will break even? Round your answer to the nearest whole number.x =Optimal Chapter-Flight FareIf exactly 192 people sign up for a charter flight, Leisure World Travel Agency charges $280/person. However, if more than 192 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Determine how many passengers will result in a maximum revenue for the travel agency. Hint: Let x denote the number of passengers above 192. Show that the revenue function R is given by R(x) = (192 + x)(280 − x). passengers: What is the maximum revenue? What would be the fare per passenger in this case?
- Aging Drivers The number of fatalities due to car crashes, based on the number of miles driven, begins to climb after the driver is past age 65. Aside from declining ability as one ages, the older driver is more fragile. The number of fatalities per 100 million vehicle miles driven is approximately N(x) = 0.0336x3 − 0.118x2 + 0.215x + 0.7 (0 ≤ x ≤ 7) where x denotes the age group of drivers, with x = 0 corresponding to those aged 50–54, x = 1 corresponding to those aged 55–59, x = 2 corresponding to those aged 60–64, …, and x = 7 corresponding to those aged 85–89.† What is the fatality rate per 100 million vehicle miles driven for an average driver in the 50–54 age group? In the 75–79 age group?How do I solve g(x)=-2(x-2)^2+5 transformation of graphsRevenue The price for a product is given byp = 100,000 - 0.1x2, where x is the number ofunits sold, so the revenue function for the product isR = px = (100,000 - 0.1x2)x.a. Find the numbers of units that must be sold to givezero revenue.b. Does the graph of the revenue function verify thissolution?
- Enter the function f(x) = x^2-2x-8 in the form f(x) = a(x-h)^2 + k , where a, h, and k are constants. Enter this function in the first box. Enter the x-coordinate of the minimum value of the function in the second box.Scenario: As the temperature increases, an experimental lubricant initially increases in flow rate, then decreases, then increases again. 1. What order polynomial model would be most appropriate for these data? (enter a whole number: 1, 2, or 3) 2. What would be the sign of b1 (enter P for positive or N for negative)13.7 f(x)=-(x^4)-(2x^3)-(9x^2)-6x Use analyticsl and graphical methods to show that the function has a maximum for some value of x in the range -2 is less than or equal to x and 1 is greater than or qual to x.
