P9.10 Optimal Output. Omaha Meat Products (OMP) produces and markets Cornhusker Plumpers, an extra-large frankfurter product being introduced on a test market basis into the St. Louis, Missouri, area. This product is similar to several others offered by OMP, and it can be produced with currently available equipment and personnel using any of three alternative production methods. Method A requires 1 hour of labor and 4 processing-facility hours to produce 100 packages of plumpers, 1 unit of Q^. Method B requires 2 labor hours and 2 processing-facility hours for each unit of Qe, and Method C requires 5 labor hours and 1 processing-facility hour for each unit of Q^. Because of slack demand for other products, OMP currently has 14 labor hours and 6 processing-facility hours available per week for producing Cornhusker Plumpers. Cornhusker Plumpers are currently being marketed to grocery retailers at a wholesale price of $1.50 per package, and demand exceeds current supply.

A. Using the equality form of the constraint conditions, set up the primal and dual linear programs that OMP would use to maximize production of Cornhusker Plumpers given currently available resources.

B. Calculate and interpret all solution values.

C. Should OMP expand its processing-facility capacity if it can do so at a cost of $40 per hour?

D. Discuss the implications of a new union scale calling for a wage rate of $20 per hour.