Laura Ralston
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Math 1111
Project Four
Laura Ralston
>
Math 1111
Project Four
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Math 1111 Project Four 50 points The total profit, P(x) in dollars for a company to manufacture and sell x items per week is given by the function P(x) = -x2 + 50x 1. How many items does the company have to sell each week to maximize its profit?
2. What is the maximum profit earned by the company in a week?
An object is projected vertically upward from the top of a building with an initial velocity of 144 ft/sec. Its distance, s(t) in feet above the ground after t seconds is given by the equation: s(t) = -16t 2 + 144t + 1003. Find the maximum height, s(t), of the object above the ground.
4. Find the height of the building, that is, at t =0.
A textile manufacturer has daily production costs of C(x) =100,000-110x+0.045x2 where C is the total cost (in dollars) and x is the number of units produced daily. 5. How many units should be produced each day to yield a minimum cost?
6. What is the daily minimum cost?
Justin wants to fence three sides of a rectangular exercise yard for his dog. The fourth side of the exercise yard will be a side of the house. Justin has 80 feet of fencing available. (RECALL: Area of a rectangle = length * width) 7. Write an equation to represent the area of the exercise yard. (HINT: It may help you to draw a picture)
8. Find the dimensions of the exercise yard that will enclose the maximum area.
9. What is the maximum area of the exercise yard?
Among all pairs of numbers whose sum is 14 10. Find a pair whose product is as large as possible.
11. What is the maximum product?
An accepted relationship between stopping distance, d (in feet) and the speed of a car, v (in mph) is d = 1.1v +0.06v 2 on dry, level concrete.12. How many feet will it take a car traveling 45 mph to stop on dry, level concrete?
13. If an accident occurs 200 feet ahead of you, what is the maximum speed you should be traveling to avoid being in the accident?
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