Perfect Stack builds standard and extralong wooden palettes for a variety of manufacturers.

Each model consists of 3 heavy separators of length equal to the palette. The standard model has 5 cross pieces above and 5 below the separators and requires 0.25 hour to assemble. The extralong version has 9 similar cross pieces on top and bottom and consumes 0.30 hour to assemble.

The supply of wood is essentially unlimited, but it requires 0.005 hour to fabricate a standard separator, 0.007 hour to fabricate an extralong separator, and 0.002 hour to fabricate a cross piece. Assuming that it can sell as many standard models as can be made at $5 profit each and as many extralongs at $7 profit, Perfect wants to decide what to produce with the available 200 hours of assembly time and 40 hours of fabrication.

(a) Formulate an operations management LP to choose an optimal plan using the decision variables x1 ! number of standard palettes assembled and sold, x2 !
number of extralongs assembled and sold, x3 ! number of standard separators manufactured, x4 ! number of extralong separators manufactured, and x5 ! number of cross pieces manufactured.

(b) Which of the constraints of your model are balance constraints? Explain.

(c) Enter and solve your model with the class optimization software.