Part a$)$

To solve the linear programming model using Excel Solver, follow these steps:

Open Excel and create a new worksheet.

Enter the given data in the worksheet.

Define decision variables X$11,$ X$12,$ X$21,$ X$22,$ X$31,$ and X$32$ in separate cells.

In another cell, enter the objective function Z $=20$X$11+25$X$21+24$X$31+32$X$12+40$X$22+48$X$32.$

Click on Data $>$ Solver.

In the Solver Parameters window, set the objective to Max, and enter the Z cell reference in the Set Objective field.

Add the constraints according to the given conditions.

Click Solve.

The Solver will provide the optimal solution.

Part b$)$

From the Solver solution, the number of reservations each location should accept for each type of car is:

Location A: Economy $-50,$ Mid$-$size $-25,$ Luxury $-75$

Location B: Economy $-50,$ Mid$-$size $-50,$ Luxury $-45$

Part c$)$

The total profit at the optimal solution is $$11,475$ per day.

Part d$)$

The shadow price for Location A is $$0,$ and for Location B is $$0\mathrm{.}04$ per car.

Part e$)$

Since the shadow price for Location B is positive, it indicates that assigning additional cars to Location B would increase the total profit. This is because the demand for cars at Location B is not fully satisfied, and there is room for more cars to generate additional profit.