Texas HP purchases high$-$performance V$8$short blocks$($part of an engine$)$ from two plants, one in Juarez, Mexico and one in New Orleans, LA$.$ They then pay shipping to their three production facilities in Dallas, Austin, and Houston. The unit purchase and shipping costs are given in Table $1.$

Table $1.$ Shipping and Manufacturing Costs per Unit

Purchase Costs

Shipping costs $($per unit$)$

Plants Dallas $($D$)$ Austin $($A$)$ Houston $($S$)$

Juarez $($J$)$ $$3200/$unit $$240/$unit $$180/$unit $$140/$unit

New Orleans $($N$)$ $$4000/$unit $$160/$unit $$120/$unit $$80/$unit

This month$$s demands at the Texas production facilities are given in Table $2.$

Table $2.$ Demand

Retail Locations Demand

Dallas $($D$)5,000$ units

Austin $($A$)3,500$ units

Houston $($H$)6,000$ units

Monthly availability of V$8$ short blocks at the plants are given in Table $3.$

Table $3.$ Plant Capacities

Plants Supply

Juarez $($J$)8,000$ units

New Orleans $($N$)9,000$ units