Profit Maximization
Creative Accountants, Ltd., is a small San Francisco-based accounting partnership specializing in the preparation of individual (I) and corporate (C) income tax returns. Prevailing prices in the local market are $125 for individual tax return preparation and $250 for corporate tax return preparation.
Five accountants run the firm and are assisted by four bookkeepers and four secretaries, all of whom work a typical 40-hour workweek. The firm must decide how to target its promotional efforts to best use its resources during the coming tax preparation season. Based on previous experience, the firm expects that an average of 1 hour of accountant time will be required for each individual return prepared. Corporate return preparation will require an average of 2 accountant-hours and 2 bookkeeper-hours. One hour of secretarial time will also be required for typing each individual or corporate return. In addition, variable computer and other processing costs are expected to average $25 per individual return and $100 per cor- porate return.
A. Set up the linear programming problem that the firm would use to determine the profit- maximizing output levels for preparing individual and corporate returns. Show both the inequality and equality forms of the constraint conditions.
B. Completely solve and interpret the solution values for the linear programming problem.
C. Calculate maximum possible net profits per week for the firm, assuming that the account- ants earn $1,500 per week, bookkeepers earn $500 per week, secretaries earn $10 per hour, and fixed overhead (including promotion and other expenses) averages $5,000 per week.
D. After considering the preceding data, one senior accountant recommended letting two bookkeepers go while retaining the rest of the current staff. Another accountant suggested that if any bookkeepers were let go, an increase in secretarial staff would be warranted. Which is the more profitable suggestion? Why?
E. Using the equality form of the constraint conditions, set up, solve, and interpret solution values for the dual linear programming problem.
F. Does the dual solution provide information useful for planning purposes? Explain.