5. Two friends, Anaira and Tommi, play a game involving two positive numbers \(x\) and \(y\) Anaira gives Tommi the following clues to see if he can correctly determine the value of \(x\) and the value of \(y\)

• \(x\) is greater than \(y\) and the difference between the two is at least 100
• \(x\) is at most 5 times as large as \(y\)
• the sum of \(2 x\) and \(3 y\) is at least 350
• the sum of \(x\) and \(y\) is as small as possible

Tommi decides to solve this problem by using the big-M method.

1. Set up an initial tableau for solving this problem using the big-M method. As part of your solution, you must show
   • how the constraints were made into equations using one slack variable, exactly two surplus variables and exactly two artificial variables
   • how the objective function was formed
   The big-M method is applied until the tableau containing the optimal solution to the problem is found. One row of this final tableau is as follows.

   b.v.	\(x\)	\(y\)	\(s _ { 1 }\)	\(S _ { 2 }\)	\(\mathrm { S } _ { 3 }\)	\(a _ { 1 }\)	\(a _ { 2 }\)	Value
   \(x\)	1	0	\(- \frac { 3 } { 5 }\)	0	\(- \frac { 1 } { 5 }\)	\(\frac { 3 } { 5 }\)	\(\frac { 1 } { 5 }\)	130

2. 1. State the value of \(x\)
   2. Hence deduce the value of \(y\), making your reasoning clear.