A car rental firm needs to relocate cars for the coming month. Three of the cities are projected to

have a surplus of cars, and three are expected to have a shortage. The following table shows the cost

$($in hundred shillings$)$ of relocating a car from a surplus city to a shortage city. Also shown are the

projected shortages and surplus for the different cities.

Surplus City

Shortage City

D Surplus Cars $1$ D$2$ D$3$

F$18610105$

F$2498120$

F$376575$

No$.$ of cars short $9065145$

Determine the number of cars to relocate from each surplus city to each shortage city so as to

minimize total relocation costs. Use the least cost cell method to find the initial basic feasible

solution and modified distribution $($MODI$)$ method to find the optimal solution.