Adog owner wants to use 200 ft of fencing to enclose the greatest possible area for his dog. he wants the fenced area to be rectangular. what dimensions should he use?

Perimeter (P) = 2 · Length(L) + 2 · Width (W) → P = 2L + 2W
Solve for either L or W (I am solving for L).
200 - 2W = 2L
(200 - 2W)/2 = L
100 - W = L

Area (A) = Length (L) · Width (W)
              = (100 - W) · W
              = 100W - W²

Find the derivative, set it equal to 0, and solve:
dA/dW = 100 - 2W
     0    = 100 - 2W
     W  = 50

refer to the equation above for L: 
100 - W = L
100 - 50 = L
        50  = L

Dimensions for the maximum Area are 50 ft x 50 ft

a: the players are you and your friend. No, there are no dominant strategies. Recall that a dominant strategy is one that yields a higher payoff regardless of the strategy chosen by the other player. In this game, if your friend plays one side, you will match that side; however, if you match, your friend will then want to change strategies, and you will therefore want to change your strategy in order to receive a higher payoff. No, there is no equilibrium. As discussed in part b, if your friend plays one side, you will match that side; however, ifyou match, your friend will then want to change strategies, and you will therefore want to change your strategy in order to receive a higher payoff

Step-by-step explanation: