Apron Outfitters is a manufacturer of aprons, jackets, and vests for a variety of occupations, including golf caddies, chefs, and carpenters. Assume that Apron Outfitters needs to schedule shipments of aprons from its three manufacturing plants to its four warehouses. The company has generated the following model using Solver Add$-$In Excel.

A data sheet for network transportation problems. The first table for cost per unit delivery has plants $12$ and $3$ in the first columns and warehouses $2$ through $4$ in columns $2$ through $5.$ The values for each plant are as follows: Plant $1$: $2\mathrm{.}69,3\mathrm{.}40,3\mathrm{.}09,2\mathrm{.}45.$ Plant $2$: $2\mathrm{.}44,3\mathrm{.}12,5\mathrm{.}08,5\mathrm{.}67.$ Plant $3$: $2\mathrm{.}02,4\mathrm{.}32,4\mathrm{.}51,3\mathrm{.}21.$ The first table for recommended shipping model has plants $12$ and $3$ in the first columns and warehouses $2$ through $4$ in columns $2$ through $5.$ Ship in column $6$ and capacity in column $8.$ The values are as follows: Plant $1$: $450,0,689,250,1389<=2000.$ Plant $2$: $200,1300,0,0,500<=1\mathrm{.}500.$ Plant $3$: $600,0,0,0,600<=600.$ Total $=4100$ Received: warehouse $1,1250$; warehouse $2,1300$; warehouse $3,689$; warehouse $4,250.$ Demand: warehouse $1,1250$; warehouse $2,1300$; warehouse $3,689$; warehouse $4,250.$ Total $=3489$ Total cost $=$ $$9,704\mathrm{.}42$; warehouse $1,$ $$2,909\mathrm{.}84$; warehouse $2,$ $$4,051\mathrm{.}39$; warehouse $3,$ $$2,129\mathrm{.}50$; warehouse $4,$ $$613\mathrm{.}69.$

The table has $4$ columns for cell, name, final value and reduced cost. The data in the table is: $D$$11,$ Plant $1$ Warehouse $1,450,0\mathrm{.}00$ $E$$11,$ Plant $1$ Warehouse $2,0,0\mathrm{.}03.$ $F$$11,$ Plant $1$ Warehouse $3,689,0\mathrm{.}00.$ $G$$11,$ Plant $1$ Warehouse $4,250,0\mathrm{.}00.$ $D$$12,$ Plant $2$ Warehouse $1,200,0\mathrm{.}00.$ $E$$12,$ Plant $2$ Warehouse $2,1300,0\mathrm{.}00.$ $F$$12,$ Plant $2$ Warehouse $3,0,2\mathrm{.}24.$ $G$$12,$ Plant $2$ Warehouse $4,0,3\mathrm{.}46.$ $D$$13,$ Plant $3$ Warehouse $1,600,0\mathrm{.}00.$ $E$$13,$ Plant $3$ Warehouse $2,0,1\mathrm{.}62.$ $F$$13,$ Plant $3$ Warehouse $3,0,2\mathrm{.}08.$ $G$$13,$ Plant $3$ Warehouse $4,0,1\mathrm{.}42.$

Using the model results, answer the following questions:

Required:

What is the total cost of the recommended shipping model?

How does total capacity compare to demand?

How many units need to be shipped from Plant $1$ to Warehouse $3?$

How much does cost need to change for Plant $2$ to ship to Warehouse $3?$