Question

The following constraints of a linear programming model have been graphed on the graph paper provided to form a feasible region:

2X    + 6Y     >=    120

10X + 2Y     > =   200

X      +     Y     <=    120

X                     <=    100

                 Y    <=      80

X,Y                  >=        0

Using the graphical method, determine the optional solution and the objective function value for the following objective functions. Graph the objective function as a dashed line on the feasible region described by the above constraints.

1. Maximize Profit: Z = 4X + 7Y, where the coefficients are the unit profit per quantity X and Y produced.

Optimal solution:                                                                                                                                                            

               

Objective Function Value at the optimal solution:                                                                                             

2. Minimize Cost:      Z = 4X + 7Y, where the coefficients are the unit cost per quantity X and Y produced.

Optimal solution:                                                                                                                                                            

               

Objective Function Value at the optimal solution:                                                                                             

Answer 1