Question $4($Transhipment problem$)$

$[16]$

Neki Sports Company manufactures treadmills in factories located in Pittsburgh and Kansas City. These are shipped to regional distribution centres in Chicago, Phoenix, and Philadelphia. Ultimately they are delivered to supply houses in New York and Los Angeles. The available supplies at the factories, demands at the final destinations, and shipping costs are illustrated in the table below.

To

$\backslash$table$[[$From$,$Chicago,Phoenix,Philadelphia,$\backslash$table$[[$New$],[$York$]],\backslash$table$[[$Los$],[$Angeles$]],$Supply$],[$Pittsburgh$,$$$4,$$$8,$$$2,-,-,1500],[$Kansas City,$$3,$$$6,$$$5,-,-,1000],[$Chicago$,-,-,-,5,7,-],[$Phoenix$,-,-,-,8,3,-],[$Philadelphia$,-,-,-,2,9,-],[$Demand$,-,-,-,1200,800,]]$

a$)$ Draw a network representation of this problem.

$(4)$

b$)$ Formulate a model to determine the number of treadmills to be shipped from each factory while minimising shipping costs.

$(12)$