Solve the following linear programming problem using the Corner Point Method:

MaxZ$=20x+30Y$

$s.t$:

$x+Y80$

$8x+9Y600$

$3x+2Y400$

$x,Y0$

a$.$ Solve the following linear programming problem using the Corner Point Method

b$.$ What is the coordinate when Constraint $1$ overlaps Constraint $2?$

c$.$ What is the solution? Justify and explain your answer.

NOTE: Please provide the relevant numerical computation to support your answers.

$[6+1+3=10$ marks $]$