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Calculus CP Optimization Review for Quiz Name: __________________________________ Date: ______________________ Period: ______ For the quiz, the following problems are fair game! - 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