Please show all work. Thanks

Problem 4. Consider the following LP. min 2x1 + 1:; I s.t. 1:1 + 1'; 5 2 x1 + 2x2 2-: 3 xhxz E l} 1] What are the shadow prices of the two constraints? Use simple: method to answer this question, and steps are required. {15 points} (Hint: ([1,2]: is an extreme point. i'ou can write its corresponding BFS and start the simplex method from this BFS} 2] If I change the coefcient of 1:1 in the objective function from 1 to 1 + o, what is the range of o. so that the optimal basis in the original LP can be kept in the new LP? Use simple: method to answer this question, and steps are required. no points} 31 If I change the right hand side of the rst constraint from 2 to 2 + it, what is the range of :1 so that the optimal basis in the original LP can be kept in the new LP':I Use simpler: method to answer this question, and steps are required. {It} points