Download Calculus CP Name: Optimization Review for Quiz Date: Period

Calculus CP
Optimization Review for Quiz
Name: __________________________________
Date: ______________________ Period: ______
For the quiz, the following problems are fair game! 
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Finding absolute maximum and absolute minimum (Section 6.1)
Finding two numbers that will maximize or minimize a sum, difference or product
Maximizing/Minimizing Area, Perimeter and Fencing
Maximizing/Minimizing Cost
Maximizing/Minimizing Enclosures (example: two by two rectangular plots)
Maximizing Volume (not on review)
To prepare, complete the practice quiz and re-do any examples/problems from worksheets!
*Round any answers to the nearest tenth*
1) A 338 m2 rectangular pea patch is to be enclosed by a fence. What dimensions for the patch will
minimize the amount of fence needed? What is the minimum amount of fence that will be needed?
2) A rectangular plot of land is enclosed by a fence and divided by a fence across its width. The total
amount of fencing used for the 4 outer sides and the dividing fence is 276 feet. Find the dimensions of
the plot of land that will maximize the area that can be enclosed in this way. What is the maximum
area?
3) A fence must be built to enclose a rectangular area of 312 square feet. Fencing costs $1.75 per foot for
two parallel sides and $2.25 per foot for the other two sides. Find the dimensions of the rectangle that
minimize the cost of the fence.
4) What is the smallest possible perimeter for a rectangle whose area of 16 square inches and what are
its dimensions?
5) Find two nonnegative numbers such that their product is 50 and the sum is the first number plus five
times the second number is a minimum.
6) The total profit (in tens of dollars) from the sale of 𝑥 hundred of boxes of candy is given by the function
𝑃(𝑥) = −𝑥 3 + 10𝑥 2 − 12𝑥.
a. Find the number of boxes of candy that should be sold in order to produce a maximum profit.
b. Find the maximum profit.
7) Solve the quadratic equation by factoring: 5𝑥 2 − 11𝑥 + 2 = 0