Revenue Maximization

Architect Elaine Benes is managing director of Designed for Sales (DFS), Inc., an Evanston, Illinois-based designer of single-family and multifamily housing units for real estate developers, building contractors, and so on. Benes' challenge is to deter- mine an optimal mix of output during the current planning period. DFS offers custom designs for single-family units, Q1: for $3,000 and custom designs for multifamily units (e.g., duplexes, fourplexes), Q2: for $2,000 each. Both types of output make use of scarce drafting, artwork, and architectural resources. Each custom design for single-family units requires 12 hours of drafting, 2 hours of artwork, and 6 hours of architectural input. Each custom design for multifamily units requires 4 hours of drafting, 5 hours of artwork, and 6 hours of archi- tectural input. Currently, DFS has 72 hours of drafting, 30 hours of artwork, and 48 hours of architectural services available on a weekly basis.

A. Using the equality form of the constraint conditions, set up the primal linear program that Benes would use to determine the sales revenue-maximizing product mix. Also set up the dual.

B. Solve for and interpret all solution values.

C. Would DFS's optimal product mix be different with a profit-maximization goal rather than a sales revenue-maximization goal? Why or why not?