Develop a LP and spreadsheet model for Problem $23$ at the end of Chapter $3$ in the Ragsdale portion of your book.

$23.$ The Rent$-$A$-$Dent car rental company allows its customers to pick up a rental car at one location and return it to any of its locations. Currently, two locations$(1$ and $2)$ have $16$ and $18$ surplus cars, respectively, and four locations $(3,4,5,$ and $6)$ each need $10$ cars. The costs of getting the surplus cars from locations $1$ and $2$ to the other locations are summarized in the following table.

Costs of Transporting Cars Between Locations

Location $3$

Location $4$ Location $5$ Location $6$

Location $1$

$$54$

$$17$

$$23$

$$30$

Location $2$

$$24$

$$18$

$$19$

$$31$

Because $34$ surplus cars are available at locations $1$ and $2,$ and $40$ cars are needed at locations $3,4,5,$ and $6,$ some locations will not receive as many cars as they need. However, management wants to make sure that all surplus cars are sent where they are needed, and that each location needing cars receives at least five.

What is the minimum transportation cost if the rental car company optimizes shipments between locations?