Please draw the graph manually and step by step clearly.

A professional musician produces pop songs and jazz songs. For each pop song and jazz song produced, the musician can get an income of $60,000 and $30,000 on average. To determine the number of pop songs (Xp) and the number of jazz songs (XJ) to produce next year for earning the most, the musician formulates an LP problem with the constraints given as follows.

Xp + XJ 20 (Constraint 1)

Xp 2XJ 0 (Constraint 2)

Xp 3XJ 12 (Constraint 3)

Xp,XJ 0

1. Determine whether (Xp = 6, XJ = 10) is a feasible solution.

2. Write the objective function of this LP problem.

3. Solve this LP problem by using the graphical method and report the optimal solution and the maximised total income (z).