Assignment:
Q1. Stephanie, the Team Manager of a soccer team, purchases many soccer balls from a retailer and sells them to all the players at her soccer club at a price of x dollars each. She can sell 600 – 15x balls per week. Find a polynomial that represents the weekly revenue for the balls. Find the revenue for a week in which the price is $12 per ball. Use the parabolic graph to illustrate the law of diminishing return, if it occurs in this case. In order for Stephanie to receive the maximum weekly revenue, how would you, as Business Manager, recommend for the price per ball?
Q2. One side of a rectangular backyard is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?
Q3. Little Johnny invested $10,000. He put part of it in a bank at 5 percent interest. He put the remainder in bonds which pay a 9 percent annual return. How much did he invest in each method (savings bank and bond) if his annual income from the two investments was $660?
Q4. Alex drove 270 miles to the University of Phoenix (UOP) in the same time as Stephanie drove 330 miles to UOP. If Stephanie drove 10 miles per hour faster than Alex, then how fast did each of them drive?
Q5. Evan, John, and Mark are on the same Learning Team at UOP. If each worked on the team assignments alone, it would take Evan 10 hours, John 8 hours, and Mark 12 hours to finish the assignments. They usually started the same time on Monday night after work. But last week, Evan started early and he worked for 2 hours on the assignments when John and Mark began. Later, all three finished the team assignments. How long did they take to finish by working together?
Q6. At the kickoff of a football game, the receiver catches the football at the left side of the goal line and runs for touchdown diagonally across the field. How many yards would he run? (Football filed is 100 yards long and 160 feet wide.)
Q7. At a large size U.S. company, the profit, y, is related to the number of Vice Presidents, x, according to the equation. What number of Vice Presidents will maximize the company profit? What is the maximum possible profit in millions?
Q8. At the Denver Broncos football game, the number of tickets sold decreases with increasing price, but the total revenue generated for the Broncos team does not necessarily decrease. Use the formula R = p(48000 – 400p) to determine the revenue when the price p of each ticket is 20 dollars and when the price p is 25 dollars. What price would produce revenue of 1.28 million dollars? Use the graph to find the price that determines the maximum revenue for this Broncos football team.
Q9. A professor found that he needed more than $2,500 per year return on his investments to live comfortably in retirement. If he invested $10,000 at 7%, how much must he invest at 9% to attain his goal?
Q10. Ken has just got a job offer and been commuting 60 miles each way to and from work. Returning home one evening, he increased his average speed 9 miles per hour above the rate on the way to work. This increase in miles per hour reduced his return time by 20 minutes. What was his average speed going to work and returning home?
Provide complete and step by step solution for the question and show calculations and use formulas.