Guidelines for solving applied minimum and maximum problems
1. Identify all given quantities and all quantities to be determined. If possible, make a sketch.
2. Write a primary equation for the quantity that is to be maximized or minimized. (A review of several useful formulas from geometry is presented inside the back cover.)
3. Reduce the primary equation to one having a single independent variable. This may involve the use of secondary equations relating the independent variables of the primary equation.
4. Determine the feasible domain of the primary equation. That is, determine the values for which the stated problem makes sense.
5. Determine the desired maximum or minimum value by the calculus techniques.
Ex. A rectangular page is to contain 20 square inches of print. The margins at the top and bottom of the page are to be 1 inch, and the margins on the left and right are to b 1. What should the dimensions of the page be so that the least amount of paper is used?
A = (x+2)(x+2)
20 = xy
A = (x+2)(20/x+2)
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