MATH 10023 Core Mathematics III Spring 2011/H1
Circle one: 9:55 12:05 Ms. Kracht
Name: Quiz Score: /20
Quiz 7: Version A
NO CALCULATORS. Show your reasoning. Use standard notation correctly.
1. (14 points) Tom purchased 62 feet of fence. He plans to create a rectangular garden using the side of the garage as
one side of the garden and fencing to border the other three sides. He wishes to enclose the largest possible garden.
(a) Sketch diagrams illustrating at least two possible such gardens.
(b) Introduce notation for the dimensions of the garden with “Let” statements. Label the diagrams above with
these variables.
(c) Write the constraint equation relating the variables. Solve it for one of the variables in terms of the other.
(d) Use a “Let” statement to introduce notation for the quantity to be optimized (maximized or minimized).
(e) Write a formula for the quantity to be optimized in terms of the dimensions of the garden and then rewrite it
as a function of just one variable.
(f) Use your formula to find the dimensions of the largest possible garden.
(g) Find the area of the largest garden.
(continued on the reverse side)
