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 $90,000$

Fort Worth $88,000$

San Diego $100,000$

Minneapolis $58,000$

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

Boulder $114,000$

Macon $124,000$

Gary $134,000$

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 $16111014$

Macon $27241718$

Gary $31122920$

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.

a$.$ Develop a transportation grid for this problem.

b$.$ Find the optimal solution using Microsoft Excel. $($Leave no cells blank $-$ be certain to enter $"0"$ wherever required.$)$