Please answer the following questions step-by-step:

Problem: Widgetco manufactures widgets at 2 factories, one in Memphis and one in Denver. The Memphis factory can produce as many as 150 widgets per day, and the Denver factory can produce as many as 230 widgets per day. Widgets are shipped by air to customers in Los Angeles and Boston. The customers in each city require 160 widgets per day. Because of the deregulation of airfares, Widgetco believes that it may be cheaper to first fly some widgets to New York or Chicago and then fly them to their final destinations, The costs of flying a widget are shown below ("---" indicates that a shipment is impossible). Widgetco wants to minimize the total cost of shipping the required widgets to its customers.

To ($)

From Memphis Denver New York Chicago Los Angeles Boston

Memphis 0 ----- 8 13 25 28

Denver ----- 0 15 12 26 25

New York ----- ----- 0 6 16 17

Chicago ----- ----- 6 0 14 16

Los Angeles ----- ----- ----- ----- 0 -----

Boston ----- ----- ----- ----- ----- 0

Solve the linear program to determine the optimal shipping plan and the optimal total cost?