- Understand the problem.
- Draw a picture.
- Which quantities are given?
- What is unknown?
- Choose the variables.
- Decide which quantity is to be maximized or minimized. Call it
Q or some name that relates to the problem.
- Choose other variables for unknown quantities and label
your diagram.
- Express Q as a function of one unknown.
- Express Q in terms of the variables in step 2. (This is your objective
function.)
- Use other information in the problem to solve for all
variables in terms of one variable (say x). (You are using the constraint
equation here.)
- Substitute for the other variables in the formula for
Q (from the preceeding step) so that x is the only variable in the formula.
Express the formula obtained in function notation: Q(x) = __
- Find the domain for the function Q(x).
- Use calculus to find the global maximum or minimum value
of Q(x) over the domain.
- Compute Q'(x) and find all critical values of Q on the domain.
(Note: Critical values are all stationary points in the domain, all points
where the derivative does not exist and endpoints if the domain is
a closed interval.)
- Evaluate Q(x) at each of the points found in the step
above.
- Compare the values to determine the maximum or minimum
value. Then determine which x gives you that Q value.
- Convert the results obtained in step 5 back into the context
of the problem. Be sure you answer the question that was asked.
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