Designed for Sales (DFS), Inc., an Evanston, Illinois-based designer of single-family and multifamily housing units for real estate developers, seeks to determine 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 (duplexes, fourplexes, etc.), 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 architectural 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?