REVIEW – Chapter 4 Maximum/Minimum Word Problems
1. A farmer has 60 feet of chicken wire to enclose a rectangular pen attached to the coop. The side of the pen along the coop is not to be fenced. What are the dimensions that will yield the maximum area of the pen?
Interpretation:
On the x-axis we are graphing .
On the y-axis we are graphing .
Work out the length:
So, what are the dimensions?
Check:
2. Find two numbers which have a difference of 28 and whose sum of squares is a minimum. What is the minimum sum of squares?
3. If a car dealership sets the price of their cars at $28 000 they will sell 52 cars. Every time they drop the price $1000, 2 more cars will be sold. What should the price of the cars be set at to maximize sales?
4. A Florida orange grower finds that the average yield/tree is 400 oranges, if no more than 16 trees are planted in each plot. For each additional tree per plot the yield of each tree is decreased by 20 oranges. How many trees should be planted in each plot to maximize yield?
5. A rectangular area is to be enclosed by a fence. Two fences, parallel to one side of the field divide the field into three equal rectangular fields. If 2000 m of fencing are available,
(a) Find the dimensions of the field giving the maximum area.
(b) Also state the maximum area.
6. Of all numbers whose sum is 50, find the two which have maximum product. Can there be a minimum product ? Explain.
7. A parabola has the equation
(a) Determine:
i. The coordinates of the vertex
ii. The direction of opening
iii. The maximum or minimum value
iv. The value of x where the maximum or minimum value occurs
(b) Sketch the graph of the parabola