Please solve and show all work.

When you arrive at Taylor Gym, the device that you've assembled is abruptly taken from you. Apparently, the device is needed as an articially intelligent judge of a competition between two groups of students. One group appears to be dressed as ancient Egyptians while the other appears to be dressed as Norsemen in the Viking Age. That's strange; why would they compete with each other? Anyway, no one seems to know the rules exactly, but by watching for a while, you start to see how it works. The competition is played out indenitely over rounds. In each round, each side has to make a move at the same time. The Egyptians have three moves: (1) etch a hieroglyphic into a piece of stone, (2) hurl an object with a catapult, or (3) pray to Ra (the sun god). The Vikings also have three moves: (a) etch a rune into a piece of wood, (b) hurl a spear, or (3) pray to 861 (the sun god). After watching for a while, you see that the AI judge awards points, depending on the pair of moves made by the two sides, according to the following table (written in terms of the points awarded to the Egyptians): Vikings Move etch hurl pray etch +4 +2 3 Egyptians hurl 1 +0 +3 pray +2 +3 2 (a) (5 points) Determine the optimal strategy for the Egyptians. (b) (5 points) Determine the optimal strategy for the Vikings. (c) (5 points) If both sides play according to their optimal strategies, then which side will win in the longrun (in the sense that they should be expected to accumulate more points over a large number of rounds of the competition)