1 - Use the dual simplex method to solve the following LP:
Max Z = -2X1 - X3
s.t. X1 + X2 - X3 >= 5
X1 - 2X2 + 4X3 >=8
X1, X2, X3 >=0
2 - Use the simplex algorithm to find the optimal solution to the following LP:
Min Z = -4X1 + X2
s.t. 3X1 + X2 <= 6
- X1 + 2X2 <=0
X1, X2 >= 0
3 - A bank has two sites at which checks are processed. Site 1 can process 10,000 checks per day, and site 2 can process 6000 checks per day. The bank processes three types of checks: vendor, salary, and personal. The processing cost per check depends on the site (table below). Each day 5000 checks of each type must be processed. Formulate a balanced transportation problem to minimize the daily cost of processing checks. Only complete formulation needs to be submitted. Do not solve.
Site1 Site2
Vendor checks 5 cents 3 cents
Salary checks 4 cents 4 cents
Personal checks 2 cents 5 cents