Applications of Maximum or Minimum John wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he
needs no fence on that side. The other three sides will be enclosed with wire fencing. If John has 750 feet of
fencing, you can find the dimensions that maximize the area of the enclosure.
a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure
(parallel to the barn). Write an function for the area A of the enclosure in terms of w. (HINT first write two
equations with w and I and A. Solve for l in one equation and substitute for l in the other).
Aw) =
b) What width w would maximize the area?
W=
ft
c) What is the maximum area?
A =
square feet
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6x - 8 = 16 solve the following equation. then place the correct number in the box provided.

Use the expression below.–4b + 8c + 12 – 8b – 2c + 6part asimplify the expression. enter your answers in the boxes. b + c + part bfactor the simplified expression using the gcf. a. 2(–2b + c + 3) b. 3(–2b + c + 3) c. 4(–2b + c + 3) d. 6(–2b + c + 3)part cwhat is the value of the expression when b = 2 and c = –3? enter your answer in the box.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.