Max Min Word Problems (ii)
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Word Problems
Maximum and Minimum Problems
You MUST set up an equation for a parabola to receive full credit for your answer. 1. The sum of two numbers is 5. Find the maximum value of their product. 2. The sum of two numbers is 18. Find the values that make the sum of their squares as small as possible. 3. A rectangular pen is made with 40m of fencing on three sides. The fourth side is a stone wall. Find the greatest possible area of such an enclosure. 4. Suppose you have 102 m of fencing to make two side by side rectangular enclosures, as shown. What are the dimensions of the largest possible area and what is the largest possible area?
5. A potato farmer has 400 bushels of potatoes that she can now sell for $3.20 per bushel. For every week whe waits, the price per bushel will drop by 10 cents but she will harvest 20 more bushels. How many weeks should she wait in order to maximize her profit? 6. An orange grower has 400 crates of fruit ready for market and will have 20 more for each day the grower waits. The present price is $60 per crate and it will drop an estimated $2 per day for each day waited. In how many days should the grower ship the crop to maximize his income? 7. In a 120 volt circuit having a resistance of 12 ohms, the power W in watts when a current I ( in amperes) is flowing is given by W = 1201 -12 I2 . For what value of I will maximum power by delivered in this circuit? 8. If an object is projected vertically upward with a velocity of 29.4m/s from a height of 30m, then its height above the ground in meters after t seconds is given by h = 30 + 29.4t - 4.9t2 . For what value oft will the object reach its maximum height? What will be its maximum height?
Maximum and Minimum Problems
You MUST set up an equation for a parabola to receive full credit for your answer. 1. The sum of two numbers is 5. Find the maximum value of their product. 2. The sum of two numbers is 18. Find the values that make the sum of their squares as small as possible. 3. A rectangular pen is made with 40m of fencing on three sides. The fourth side is a stone wall. Find the greatest possible area of such an enclosure. 4. Suppose you have 102 m of fencing to make two side by side rectangular enclosures, as shown. What are the dimensions of the largest possible area and what is the largest possible area?
5. A potato farmer has 400 bushels of potatoes that she can now sell for $3.20 per bushel. For every week whe waits, the price per bushel will drop by 10 cents but she will harvest 20 more bushels. How many weeks should she wait in order to maximize her profit? 6. An orange grower has 400 crates of fruit ready for market and will have 20 more for each day the grower waits. The present price is $60 per crate and it will drop an estimated $2 per day for each day waited. In how many days should the grower ship the crop to maximize his income? 7. In a 120 volt circuit having a resistance of 12 ohms, the power W in watts when a current I ( in amperes) is flowing is given by W = 1201 -12 I2 . For what value of I will maximum power by delivered in this circuit? 8. If an object is projected vertically upward with a velocity of 29.4m/s from a height of 30m, then its height above the ground in meters after t seconds is given by h = 30 + 29.4t - 4.9t2 . For what value oft will the object reach its maximum height? What will be its maximum height?
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