Bindley Corporation has a one$-$year contract to supply motors for all washing machines produced by Rinso Ltd$.$ Rinso manufactures the washers at four locations around the country: New York City, Fort Worth, San Diego, and Minneapolis. Plans call for the following numbers of washing machines to be produced at each location:

New York City $55,000$

Fort Worth $71,000$

San Diego $75,000$

Minneapolis $75,000$

Bindley has three plants that can produce the motors. The plants and production capacities are

Boulder $110,000$

Macon $80,000$

Gary $165,000$

Due to varying production and transportation costs, the profit Bindley earns on each $1,000$ units depends on where they were produced and where they were shipped. The following table gives the accounting department estimates of the dollar profit per unit. $($Shipment will be made in lots of $1,000.)$

SHIPPED TO

PRODUCED AT NEW YORK CITY FORT WORTH SAN DIEGO MINNEAPOLIS

Boulder $7151114$

Macon $26181011$

Gary $10221715$

Given profit maximization as a criterion, Bindley would like to determine how many motors should be produced at each plant and how many motors should be shipped from each plant to each destination.