Problem $14-7($Algo$)$

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 $50,000$

Fort Worth $72,000$

San Diego $55,000$

Minneapolis $93,000$

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

Boulder $90,000$

Macon $100,000$

Gary $80,000$

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 $1,000.)$

PRODUCED AT SHIPPED TO

NEW YORK CITY FORT WORTH SAN DIEGO MINNEAPOLIS

Boulder $812914$

Macon $1311711$

Gary $10131117$

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.