Question 1, Graphical solution

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 (Graph paper is provided

on the next page). 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.