Consider the following LP problem:

a) Solve the above LP problem using suitable algorithms.

b) Exhibit the optimal primal and dual solutions and the optimal primal and dual bases.

c) Verify that the complementary slackness conditions hold for the optimal primal and dual solutions.

d) Compute the opportunity cost of activity 3 at market prices and at factor costs and state by how much the price of commodity 3 should increase to make it profitable.

max Z=3x+2x2 +423 sub ect to 21 22+3x3 -1 -21+222 + 23 3 xj 20, j=1,..., 3.