Consider the following LP problem:

Maximize profit = 10X1 + 8X2

Subject to 4X1 + 2X2 ≤ 80

X1 + 2X2 ≤ 50

X1, X2 ≥ 0

(a) Solve this problem graphically.

(b) Set up the initial simplex tableau. On the graph, identify the corner point represented by this tableau.

(c) Select the pivot column. Which variable is the entering variable?

(d) Compute the ratio of the quantity-to-pivot column substitution rate for each row. Identify the points on the graph related to these ratios.

(e) How many units of the entering variable will be brought into the solution in the second tableau? What would happen if the largest ratio rather than the smallest ratio were selected to determine this (see the graph)?

(f) Which variable is the leaving variable? What will the value of this variable be in the next tableau?

(g) Finish solving this problem using the simplex algorithm.

(h) The solution in each simplex tableau is a corner point on the graph. Identify the corner point associated with each tableau.