How many different solutions are there to the equation x+y+z=15 subject to the following constraints ... • must be an integer and x > 2 • y must be an integer and y > 3 • z must be an integer and z> 4

Pivot once about the circled element in the simplex tableau, and read the solution from the result. x1 x2 x3 s1 2 83 2 0 이 14 이 36 이 18 0 10 1 2 0 1 2. 3 -2 -1 -3 O A. X3 = 14, s2 = 12, s3 = 4, z = 42; x,, X2, S, = 0 %3D OB. X3 = 14, s2 = 12, s3 = -4, z = 42; x4, X2, S, = 0 OC. X3 = 14, s2 = - 12, s3 = 4, z = - 42; x1, X2, S1 = 0 O D. X3 = 14, s2 = -6, s3 = 4, z = 42; x4, X2, S1 = 0 %3D

a.) Make a list of the amounts of money one can have that cannot be reduced to a smaller number of coins. (Hint: there are seven possible amounts.) One of the amounts is (d+e). b.) Make an addition table for Glosian money. It should be a seven by seven table, with a row and column for each of the amounts you found in the previous problem. For example, your table shouldshow that (d+e)+d=f c.) One of the seven amounts you found in the previous problem can be considered to be the zero of Glosian money, since adding it to a collection of coins does not change the collection’s value (after trading to get the  smallest possible number of coins, of course.) Which amount is the zero forGlosian money? d.) The opposite of an amount is the amount you add to it to get the zero. Find the opposite of each of the seven amounts.

Without graphing or solving the following, determine if the solutions to the equations will have one solution, no solution, or infinitely many solutions (y= ²/3 x + 5 y = ²/x-5 15): d. e. { y = ²x + 5 (5y = 4x + 25 15a) 15b)

1. Does the equation 6x +12y + 48z = 308 have any solutions such that x = Z, y = Z, and z € Z? If yes, provide one. If not, explain your answer.