A rectangular garden will be fenced off with 220 feet of available material . Wh
ID: 3288477 • Letter: A
Question
A rectangular garden will be fenced off with 220 feet of available material . What is the largest area that can be fenced off? Do the
following to answer this question .
(1) Draw a picture of the garden and label the key dimensions .
(2) List all the known and unknown quantities related to the garden and assign each a variable .
(3) Write two or more equations relating the variables listed above. Be sure that one of them involves the quantity that is being optimized. Label this one the primary equation.
(4) Does the primary equation have two or more independent variable ? If so, how can we rewrite it so that it contains only one independent variable? Hint: Can you make use of the other equation(s) you wrote in question 3?
(5) We have previously seen that extrema, optimal values, occur when the derivative of a function equals zero . So, take the derivative of the primary equation from question 4, set it equal to zero and solve for the unknown variable . What information do you now have? Does this answer the initial question asked? If not, how can we use this value to get to the answer we need ?
(6) What is the answer to the question asked?
Explanation / Answer
Perimeter = 220 = 2*(L+B) => L+B=110
Area =A= L*B =(110-L)*L=110L-L^2
For max, dA/dL = 0
=> 110-2L=0=>L= 55
A= 3025