For the following problem, formulate the LP$.$ DO NOT SOLVE. $($Hint: Double Scripted

Variables$)$

$4.$ The Roadnet Transport Company expanded its shipping capacity by purchasing $90$ trailer

trucks from a bankrupt competitor. The company subsequently located $30$ of the

purchased trucks at each of its shipping warehouses in Charlotte, Memphis, and

Louisville. The company makes shipments from each of these warehouses to terminals in

St$.$ Louis, Atlanta, and New York. Each truck is capable of making one shipment per

week. The terminal managers have indicated their capacity for extra shipments. The

manager at St$.$ Louis can accommodate $40$ additional trucks per week, the manager at

Atlanta can accommodate $28$ additional trucks, and the manager at New York can

accommodate $29$ additional trucks. The company makes the following profit per

truckload shipment from each warehouse to each terminal. The profits differ as a result of

differences in products shipped, shipping costs, and transport rates:

Warehouse St$.$ Louis Atlanta New York

Charlotte $$1800$ $$2050$ $$1950$

Memphis $15209501010$

Louisville $11508602300$

The company wants to know how many trucks to assign to each route $($i$.$e$.,$ warehous