Question $5-25$ marks

A firm manufacturing a single product and has factories in Glenfield, Manukau and Avondale. The factories have produced $60,35$ and $40$ units respectively during this month. The firm made a commitment to sell $2$ units to customer A$,45$ to customer B$,20$ units to customer $C,18$ units to customer $D$ and $30$ units to customer $E.$ The cost of shipping units to customers from plants is shown below. Determine the optimal export mix in minimising the total transportation cost.

$\backslash$table$[[$Unit Inventory$],[\backslash$table$[[,$Glenfield,$60],[,$Manukau,$35],[,$Avondale,$40]],,]]$

$\backslash$table$[[,$ping costs$],[,$Customer,A$,$B$,$C$,$D$,E$