No missing informatio !! PLEASE IF YOU CAN DO IT PERFECTLY HELP ME IF NOT ALLOW OTHER TUTORS TO HELP ME ! PLEASE ANSWER EACH OF THE HELP COMPLETELY (5 EXERCISES EACH HELP) HELP 1: Maximize and minimize functions Determine and interpret the maximum or minimum of a quadratic function. For each of the questions, determine and correctly interpret the maximum or minimum of the functions that model the following situations using valid mathematical procedures and correct mathematical notation. 1. The profits of a small company are related to the price of its only product. The relationship is \ R(p) = - 0.4p ^ 2 + 64p-2400, where R is the income in thousands of dollars and p is the price of the product in dollars. What price would maximize income? 2. A rocket is fired from the top of a platform. Its height h, in meters, above the ground, after t seconds, is given by the function h(t) = - 5t ^ 2 + 10t + 20. a. What is the maximum height reached by the rocket? b. How long did it take you to reach maximum height? 3. The owner of a soft drink factory knows that his profit in thousands of dollars per week, as a function of the number x of cases of soft drinks sold, is given by the equation U = -0.01x ^ 2 + 9x-1296. a. How many boxes must be sold weekly to make a maximum profit? b. What is the maximum profit? 4. For a certain company, the monthly profits obtained by investing x dollars a month in advertising are given by U = -0.12x ^ 2 + 510x-25000. How much should they invest in advertising to maximize their profits? 5. The effectiveness of a television commercial depends on how many times a person watches it. After some experiments, an advertising agency found that if E effectiveness is measured on a scale of 0 to 10, then ****** SEE ATTACHED PHOTO OF THE EXERCISE**** where n is the number of times a person sees a particular commercial ad. For an ad to be most effective, how many times must a person see it? HELP 2: Application problems: breakeven points, revenues, costs and profits. 1. A company sells portable radios. The cost equation to manufacture the product is given by C (x) = x ^ 2-x + 31. The company sells its radios for $ 3.00 each. Therefore, your income equation is R \ left (x \ right) = 3x, where R is income and x is the number of units sold in the week (in thousands). Find and interpret the equilibrium point. 2. The supply and demand equations for a certain product are: (1) and (2) respectively, where p represents the price per unit in dollars and q, the number of units sold per period. (1)3q-200p + 1800 = 0 (2)3q + 100p-1800 = 0 Find the equilibrium price algebraically. Find and interpret the equilibrium price when a tax of 27 cents per unit is imposed on the supplier. 3. A basketball team plays in a stadium with a capacity of 55,000 spectators. With the ticket price at $ 10, the average attendance in recent games has been 27,000. Market research indicates that for every dollar the ticket price goes down, attendance will increase by 3,000. Identify the function that maximizes ticket sales revenue. 4. The demand function for the manufacturer of a product is p = f (q) = 200-5q, where p is the price (in dollars) per unit when q units are demanded (per week). a. Identify the function that maximizes the manufacturer's total revenue. b. Determine this income. 5. The total monthly income of a nursery for the care of x children is given by r = 450x, and its total monthly costs are c = 380x + 3500. a. How many children need to enroll each month to break even? b. In other words, when does income equal costs