Consider the following linear program.

Max	2A + 3B
s.t.
	5A + 5B		410	Constraint 1
	1A + 1B		10	Constraint 2
	1A + 3B		90	Constraint 3
	A, B 0

The figure shows a graph of the constraint lines.

The A B-coordinate plane is given. There are 3 lines on the graph.

• The first line enters the window at B = 82 on the positive B-axis, goes down and right, passes through the point (36, 46) crossing the second line, passes through the point (78, 4) crossing the third line, and exits the window at A = 82 on the positive A-axis.
• The second line enters the window at B = 10 on the positive B-axis, goes up and right, passes through the point (15, 25) crossing the third line, passes through the point (36, 46) crossing the first line, and exits the window in the first quadrant.
• The third line enters the window at B = 30 on the positive B-axis, goes down and right, passes through the point (15, 25) crossing the second line, passes through the point (78, 4) crossing the first line, and exits the window at A = 90 on the positive A-axis.

(a)

Place a number (1, 2, or 3) next to each constraint line to identify which constraint it represents. Select the correct graph.

The A B-coordinate plane is given. There are 3 lines on the graph.

• The line labeled (1) enters the window at B = 82 on the positive B-axis, goes down and right, passes through the point (36, 46) crossing the line labeled (2), passes through the point (78, 4) crossing the line labeled (3), and exits the window at A = 82 on the positive A-axis.
• The line labeled (2) enters the window at B = 10 on the positive B-axis, goes up and right, passes through the point (15, 25) crossing the line labeled (3), passes through the point (36, 46) crossing the line labeled (1), and exits the window in the first quadrant.
• The line labeled (3) enters the window at B = 30 on the positive B-axis, goes down and right, passes through the point (15, 25) crossing the line labeled (2), passes through the point (78, 4) crossing the line labeled (1), and exits the window at A = 90 on the positive A-axis.

The A B-coordinate plane is given. There are 3 lines on the graph.

• The line labeled (3) enters the window at B = 82 on the positive B-axis, goes down and right, passes through the point (36, 46) crossing the line labeled (1), passes through the point (78, 4) crossing the line labeled (2), and exits the window at A = 82 on the positive A-axis.
• The line labeled (1) enters the window at B = 10 on the positive B-axis, goes up and right, passes through the point (15, 25) crossing the line labeled (2), passes through the point (36, 46) crossing the line labeled (3), and exits the window in the first quadrant.
• The line labeled (2) enters the window at B = 30 on the positive B-axis, goes down and right, passes through the point (15, 25) crossing the line labeled (1), passes through the point (78, 4) crossing the line labeled (3), and exits the window at A = 90 on the positive A-axis.

The A B-coordinate plane is given. There are 3 lines on the graph.

• The line labeled (3) enters the window at B = 82 on the positive B-axis, goes down and right, passes through the point (36, 46) crossing the line labeled (2), passes through the point (78, 4) crossing the line labeled (1), and exits the window at A = 82 on the positive A-axis.
• The line labeled (2) enters the window at B = 10 on the positive B-axis, goes up and right, passes through the point (15, 25) crossing the line labeled (1), passes through the point (36, 46) crossing the line labeled (3), and exits the window in the first quadrant.
• The line labeled (1) enters the window at B = 30 on the positive B-axis, goes down and right, passes through the point (15, 25) crossing the line labeled (2), passes through the point (78, 4) crossing the line labeled (3), and exits the window at A = 90 on the positive A-axis.

The A B-coordinate plane is given. There are 3 lines on the graph.

• The line labeled (2) enters the window at B = 82 on the positive B-axis, goes down and right, passes through the point (36, 46) crossing the line labeled (3), passes through the point (78, 4) crossing the line labeled (1), and exits the window at A = 82 on the positive A-axis.
• The line labeled (3) enters the window at B = 10 on the positive B-axis, goes up and right, passes through the point (15, 25) crossing the line labeled (1), passes through the point (36, 46) crossing the line labeled (2), and exits the window in the first quadrant.
• The line labeled (1) enters the window at B = 30 on the positive B-axis, goes down and right, passes through the point (15, 25) crossing the line labeled (3), passes through the point (78, 4) crossing the line labeled (2), and exits the window at A = 90 on the positive A-axis.

(b)

Shade in the feasible region. Select the correct graph.

The A B-coordinate plane is given. There are 3 lines and a shaded region on the graph.

• The first line enters the window at B = 82 on the positive B-axis, goes down and right, passes through the point (36, 46) crossing the second line, passes through the point (78, 4) crossing the third line, and exits the window at A = 82 on the positive A-axis.
• The second line enters the window at B = 10 on the positive B-axis, goes up and right, passes through the point (15, 25) crossing the third line, passes through the point (36, 46) crossing the first line, and exits the window in the first quadrant.
• The third line enters the window at B = 30 on the positive B-axis, goes down and right, passes through the point (15, 25) crossing the second line, passes through the point (78, 4) crossing the first line, and exits the window at A = 90 on the positive A-axis.
• The region is below the first line, below the second line, and below the third line.

The A B-coordinate plane is given. There are 3 lines and a shaded region on the graph.

• The first line enters the window at B = 82 on the positive B-axis, goes down and right, passes through the point (36, 46) crossing the second line, passes through the point (78, 4) crossing the third line, and exits the window at A = 82 on the positive A-axis.
• The second line enters the window at B = 10 on the positive B-axis, goes up and right, passes through the point (15, 25) crossing the third line, passes through the point (36, 46) crossing the first line, and exits the window in the first quadrant.
• The third line enters the window at B = 30 on the positive B-axis, goes down and right, passes through the point (15, 25) crossing the second line, passes through the point (78, 4) crossing the first line, and exits the window at A = 90 on the positive A-axis.
• The region is below the first line, below the second line, and above the third line.

The A B-coordinate plane is given. There are 3 lines and a shaded region on the graph.

• The first line enters the window at B = 82 on the positive B-axis, goes down and right, passes through the point (36, 46) crossing the second line, passes through the point (78, 4) crossing the third line, and exits the window at A = 82 on the positive A-axis.
• The second line enters the window at B = 10 on the positive B-axis, goes up and right, passes through the point (15, 25) crossing the third line, passes through the point (36, 46) crossing the first line, and exits the window in the first quadrant.
• The third line enters the window at B = 30 on the positive B-axis, goes down and right, passes through the point (15, 25) crossing the second line, passes through the point (78, 4) crossing the first line, and exits the window at A = 90 on the positive A-axis.
• The region is below the first line, above the second line, and above the third line.

The A B-coordinate plane is given. There are 3 lines and a shaded region on the graph.

• The first line enters the window at B = 82 on the positive B-axis, goes down and right, passes through the point (36, 46) crossing the second line, passes through the point (78, 4) crossing the third line, and exits the window at A = 82 on the positive A-axis.
• The second line enters the window at B = 10 on the positive B-axis, goes up and right, passes through the point (15, 25) crossing the third line, passes through the point (36, 46) crossing the first line, and exits the window in the first quadrant.
• The third line enters the window at B = 30 on the positive B-axis, goes down and right, passes through the point (15, 25) crossing the second line, passes through the point (78, 4) crossing the first line, and exits the window at A = 90 on the positive A-axis.
• The region is below the first line, above the second line, and below the third line.

(c)

Identify the optimal extreme point. What is the optimal solution?

(A, B) =

78,4

(d)

Which constraints are binding? Explain.

The optimal solution occurs at the intersection of constraints ---Select--- 1 and 2 2 and 3 1 and 3 , so these are the binding constraints.

(e)

How much slack or surplus is associated with the nonbinding constraint?

Constraint ? 1 2 3 is the nonbinding constraint. There is a ---Select--- slack surplus of associated with this constraint.