Refer to the divide-and-choose method for two players presented in Section 4.1. Referen...

Refer to the divide-and-choose method for two players presented in Section 4.1.

Reference:

DIVIDE-AND-CHOOSE METHOD FOR TWO PLAYERS

Two players, X and Y, are to divide a cake.

STEP 1: Player X divides the cake into two pieces that he or she considers of equal value. (We call player X the divider.)

STEP 2: Player Y picks whichever of the two pieces he or she considers to be of greater value. If player Y also considers the pieces to be of equal value, then he or she can pick either piece. (We call player Y the chooser.)

STEP 3: Player X gets the piece that player Y did not select.

Alaina and Marie want ice cream for dessert. There are 5 ounces of mint chip ice cream left in one container and 6 ounces of fudge swirl left in another container. Alaina will serve the ice cream. Because she prefers mint chip to fudge by a ratio of 2 to 1, she puts 3 ounces of mint chip and 2 ounces of fudge swirl in one bowl and the remaining ice cream in the other bowl. Because Alaina divided the ice cream into two bowls, Marie will choose which bowl she wants. She prefers mint chip to fudge swirl in a ratio of 3 to 2.

a. What value will Alaina place on each bowl of ice cream?

b. What value will Marie place on each bowl of ice cream, and which bowl will she choose?

c. Is this division of the ice cream proportional? Explain.

d. Is this division envy-free? Explain.