Consider the following linear program.

Max2A+ 3B

s.t.

5A+ 5B350Constraint 11A+ 1B10Constraint 21A+ 3B90Constraint 3A,B0

The figure shows a graph of the constraint lines.

TheAB-coordinate plane is given. There are 3 lines on the graph.

• The first line enters the window atB= 70on the positiveB-axis,goes down and right, passes through the point(30, 40)crossing the second line, passes through the point(60, 10)crossing the third line, and exits the window atA= 70on the positiveA-axis.
• The second line enters the window atB= 10on the positiveB-axis,goes up and right, passes through the point(15, 25)crossing the third line, passes through the point(30, 40)crossing the first line, and exits the window in the first quadrant.
• The third line enters the window atB= 30on the positiveB-axis,goes down and right, passes through the point(15, 25)crossing the second line, passes through the point(60, 10)crossing the first line, and exits the window atA= 90on the positiveA-axis.

(a)

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

TheAB-coordinate plane is given. There are 3 lines on the graph.

• The line labeled (3) enters the window atB= 70on the positiveB-axis,goes down and right, passes through the point(30, 40)crossing the line labeled (1), passes through the point(60, 10)crossing the line labeled (2), and exits the window atA= 70on the positiveA-axis.
• The line labeled (1) enters the window atB= 10on the positiveB-axis,goes up and right, passes through the point(15, 25)crossing the line labeled (2), passes through the point(30, 40)crossing the line labeled (3), and exits the window in the first quadrant.
• The line labeled (2) enters the window atB= 30on the positiveB-axis,goes down and right, passes through the point(15, 25)crossing the line labeled (1), passes through the point(60, 10)crossing the line labeled (3), and exits the window atA= 90on the positiveA-axis.

TheAB-coordinate plane is given. There are 3 lines on the graph.

• The line labeled (2) enters the window atB= 70on the positiveB-axis,goes down and right, passes through the point(30, 40)crossing the line labeled (3), passes through the point(60, 10)crossing the line labeled (1), and exits the window atA= 70on the positiveA-axis.
• The line labeled (3) enters the window atB= 10on the positiveB-axis,goes up and right, passes through the point(15, 25)crossing the line labeled (1), passes through the point(30, 40)crossing the line labeled (2), and exits the window in the first quadrant.
• The line labeled (1) enters the window atB= 30on the positiveB-axis,goes down and right, passes through the point(15, 25)crossing the line labeled (3), passes through the point(60, 10)crossing the line labeled (2), and exits the window atA= 90on the positiveA-axis.

TheAB-coordinate plane is given. There are 3 lines on the graph.

• The line labeled (1) enters the window atB= 70on the positiveB-axis,goes down and right, passes through the point(30, 40)crossing the line labeled (2), passes through the point(60, 10)crossing the line labeled (3), and exits the window atA= 70on the positiveA-axis.
• The line labeled (2) enters the window atB= 10on the positiveB-axis,goes up and right, passes through the point(15, 25)crossing the line labeled (3), passes through the point(30, 40)crossing the line labeled (1), and exits the window in the first quadrant.
• The line labeled (3) enters the window atB= 30on the positiveB-axis,goes down and right, passes through the point(15, 25)crossing the line labeled (2), passes through the point(60, 10)crossing the line labeled (1), and exits the window atA= 90on the positiveA-axis.

TheAB-coordinate plane is given. There are 3 lines on the graph.

• The line labeled (3) enters the window atB= 70on the positiveB-axis,goes down and right, passes through the point(30, 40)crossing the line labeled (2), passes through the point(60, 10)crossing the line labeled (1), and exits the window atA= 70on the positiveA-axis.
• The line labeled (2) enters the window atB= 10on the positiveB-axis,goes up and right, passes through the point(15, 25)crossing the line labeled (1), passes through the point(30, 40)crossing the line labeled (3), and exits the window in the first quadrant.
• The line labeled (1) enters the window atB= 30on the positiveB-axis,goes down and right, passes through the point(15, 25)crossing the line labeled (2), passes through the point(60, 10)crossing the line labeled (3), and exits the window atA= 90on the positiveA-axis.

(b)

Shade in the feasible region. Select the correct graph.

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

• The first line enters the window atB= 70on the positiveB-axis,goes down and right, passes through the point(30, 40)crossing the second line, passes through the point(60, 10)crossing the third line, and exits the window atA= 70on the positiveA-axis.
• The second line enters the window atB= 10on the positiveB-axis,goes up and right, passes through the point(15, 25)crossing the third line, passes through the point(30, 40)crossing the first line, and exits the window in the first quadrant.
• The third line enters the window atB= 30on the positiveB-axis,goes down and right, passes through the point(15, 25)crossing the second line, passes through the point(60, 10)crossing the first line, and exits the window atA= 90on the positiveA-axis.
• The region is below the first line, above the second line, and below the third line.

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

• The first line enters the window atB= 70on the positiveB-axis,goes down and right, passes through the point(30, 40)crossing the second line, passes through the point(60, 10)crossing the third line, and exits the window atA= 70on the positiveA-axis.
• The second line enters the window atB= 10on the positiveB-axis,goes up and right, passes through the point(15, 25)crossing the third line, passes through the point(30, 40)crossing the first line, and exits the window in the first quadrant.
• The third line enters the window atB= 30on the positiveB-axis,goes down and right, passes through the point(15, 25)crossing the second line, passes through the point(60, 10)crossing the first line, and exits the window atA= 90on the positiveA-axis.
• The region is below the first line, below the second line, and below the third line.

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

• The first line enters the window atB= 70on the positiveB-axis,goes down and right, passes through the point(30, 40)crossing the second line, passes through the point(60, 10)crossing the third line, and exits the window atA= 70on the positiveA-axis.
• The second line enters the window atB= 10on the positiveB-axis,goes up and right, passes through the point(15, 25)crossing the third line, passes through the point(30, 40)crossing the first line, and exits the window in the first quadrant.
• The third line enters the window atB= 30on the positiveB-axis,goes down and right, passes through the point(15, 25)crossing the second line, passes through the point(60, 10)crossing the first line, and exits the window atA= 90on the positiveA-axis.
• The region is below the first line, above the second line, and above the third line.

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

• The first line enters the window atB= 70on the positiveB-axis,goes down and right, passes through the point(30, 40)crossing the second line, passes through the point(60, 10)crossing the third line, and exits the window atA= 70on the positiveA-axis.
• The second line enters the window atB= 10on the positiveB-axis,goes up and right, passes through the point(15, 25)crossing the third line, passes through the point(30, 40)crossing the first line, and exits the window in the first quadrant.
• The third line enters the window atB= 30on the positiveB-axis,goes down and right, passes through the point(15, 25)crossing the second line, passes through the point(60, 10)crossing the first line, and exits the window atA= 90on the positiveA-axis.
• The region is below the first line, below the second line, and above the third line.

(c)

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

(A,B) =

(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---

surplus

slack

ofassociated with this constraint.