Max Min Word Problems (iii)

Maximum and Minimum Problems 1. A fanner wants to make a rectangular enclosure using a wall as one side and 120 m of fencing for the other 3 sides. Find the value of x that gives the greatest area?

2. A rectangle has a perimeter of 80 cm. If its width is x, express its length and its area in terms of x. What is the maximum area of the rectangle?

3. Suppose you have 102 m of fencing to make two side-by-side rectangular enclosures as shown, What is the maximum area you can enclose?

4. If a ball is thrown vertically upward at 30 m/s, then its approximate height in meters t seconds later is given by h(tO = 30t - 5t2. a.) How high does the ball get? b.) How many seconds does it take to reach its highest point? c.) After how many seconds does the ball hit the ground?

5. If a ball is thrown upward from a building 30 m tall and the ball has a vertical velocity of 25 m/s, then it approximate height above the ground t seconds later is given by:

h(t) = 30 + 25t - 5t 2 . a.) How high does the ball go? b..) How many seconds does it take to reach its highest point? c.) After how many seconds does the ball hit the ground? 6. Find the number of units that produces a maximum revenue given by R = 900x - .lx 2 , where R is the total revenue in dollars and x is the number of units sold.

7. Let x be the amount (in hundreds of dollars) a company spends on advertising, and let P be the profit where P = 230 + 20x - .5x 2 . What expenditure for advertising results in the maximum profit?