a$.$ To develop a transportation grid for this problem, we need to create a matrix where rows represent the plants and columns represent the destinations. Each cell will represent the profit earned per unit when a motor is produced at the corresponding plant and shipped to the respective destination.

Here's the transportation grid:

$```$

New York City Fort Worth San Diego Minneapolis

Boulder $16111014$

Macon $27241718$

Gary $31122920$

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b$.$ To find the optimal solution using Microsoft Excel, we can use the Solver add$-$in$.$ However, since I can't interact with Excel directly, I'll provide you with the steps to set up and solve this problem using Solver:

$1.$ Enter the profit matrix in Excel.

$2.$ Set up decision variables:

$-$ Define variables for the number of motors produced at each plant and shipped to each destination.

$3.$ Set up constraints:

$-$ Supply constraints: The total number of motors produced at each plant should not exceed its capacity.

$-$ Demand constraints: The total number of motors shipped to each destination should meet the demand.

$-$ Non$-$negativity constraints: The number of motors produced and shipped should be non$-$negative.

$4.$ Set up the objective function: Maximize the total profit by summing the products of the decision variables and their corresponding profits.

$5.$ Use Solver to find the optimal solution by maximizing the objective function, subject to the constraints.

Once you set up the model in Excel, you can use Solver to find the optimal solution. If you encounter any specific issues or need further assistance with the Excel setup, feel free to ask!