Question 1, Graphical solution (15 marks)

For a linear programming model given below:

Decision variables

x1 Number of trucks to produce.

x2 - Number of cars to produce.

Objective function

Maximize z = 3x1 +2 x2

Constraints

Constraint A: 3x1 + 2x2 120

Constraint B: x1 + x2 50

Constraint C: x1 30

Constraint D: x2 5

Non-negativity: x1, x2 0

Solve this linear programming model by using the graphical approach.

For your graphical solution,

Label the axes.

Draw and label each constraint. Show your procedure of drawing Constraint A.

For each constraint line, determine and label which side is feasible. Briefly explain how to determine the feasible side for Constraint A.

Shade and label the feasible region.

Identify all feasible corner points and determine the coordinates of each feasible corner point.

Show your calculations for the corner point determined by Constraints A and B.

Determine the optimal solution and objective function value using graphical method.