Leading computer hardware manufacturer, Dull Inc, is expanding its distribution network and planning to open a number of new warehouses to service three retail regions. The three warehouse sites under consideration, A, B & C, have the following estimated monthly fixed costs $50,000, $45,000 and $47,500 respectively. The three retail centres have anticipated demands as follow: region 1 requires 950 units per month, region 2 requires 850 units per month, and region 3 requires 650 units per month. The table below shows the costs of sending 1 item from each warehouse to the three regions and the quantity each warehouse can supply. The company wishes to meet monthly demands at minimum cost, subject to following constraints:

a) At most 2 warehouses must be opened.

b) If warehouse B is opened, then warehouse A must also be opened.

Formulate an LP that can be used to minimise the monthly costs of meeting demand. Use an if-then constraint in the formulation of the constraint (b) above. Find the optimal solution using POM/QM and state the outcomes.