Solve the following LP problem by graphical methods (label the axes). Be as accurate as possible. Choose the “right” scale for your axes.

a) Read the (approximate) values of the variables x1 and x2 off your diagram. Evaluate the ob ective function at the optimal values of x1 and x2.

b) Set up the total cost function and derive the marginal cost of activities 1 and 2, respectively. Derive average costs for those activities and verify that marginal cost is equal to average cost (assume that xj > 0, j = 1, 2).

c) Set up the dual problem and solve it by using the information derived from the primal and dual complementary slackness conditions.

d) Verify that the optimal value of the primal ob ective function is equal to the optimal value of the dual ob ective function.

max TR 41 + 3x2 sub ect to 21 16 12 8 21 222 10, 20 24