Wobbly Office Equipment (WOE) makes two models of tables for libraries and other university facilities. Both models use the same tabletops, but model A has 4 short (18-inch) legs and model B has 4 longer ones (30-inch). It takes 0.10 labor hour to cut and shape a short leg from stock, 0.15 labor hour to do the same for a long leg, and 0.50 labor hour to produce a tabletop.

An additional 0.30 labor hour is needed to attach the set of legs for either model after all parts are available. Estimated profit is $30 for each model A sold and $45 for each model B. Plenty of top material is on hand, but WOE wants to decide how to use the available 500 feet of leg stock and 80 labor hours to maximize profit, assuming that everything made can be sold.

(a) Formulate an operations management LP to choose an optimal plan using the decision variables x1 ! number of model A’s assembled and sold, x2 ! number of model B’s assembled and sold, x3 !

number of short legs manufactured, x4 !

number of long legs manufactured, and x5 ! number of tabletops manufactured.

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

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