Profit Maximization. Samantha Spade & Associates, Ltd. is a small architectural firm located in Portland, Oregon, specializing in the preparation of multi-family residential housing complex, R, and commercial retails, C, architectural designs. Prevailing prices in the market are $10,000 for residential housing designs and $25,000 for commercial retail designs.
Six architects run the firm, and work a 50-hour workweek, 50 weeks per year. They are assisted by six drafting personnel and two secretaries, all of whom work a typical 40-hour workweek, 50 weeks per year. The firm must decide how to target its promotional efforts so as to best use its resources during the coming year. Based on previous experience, the firm expects that an average of 150 hours of architect and 100 hours of drafting time will be required for each residential housing complex design, whereas commercial retail design will require an average of 250 architect hours and 200 drafting hours. Fifty hours of secretarial time will also be required for each architectural design. In addition, variable computer and other processing costs are expected to average $1,000 per residential design and $1,500 per commercial retail design.
A. Set up the linear programming problem the firm would use to determine the profit-maximizing output levels for residential and commercial designs. 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 year for the firm assuming that architects draw a salary of $100,000 per year, drafting personnel earn $65,000 per year, secretaries are paid $20 per hour, and fixed overhead (including promotion and other expenses) averages $50,000.
D. After considering the above data, one senior architect recommended reducing one drafting personnel to part-time status (adjusting salary accordingly) while retaining the rest of the current staff full-time. What are net profits per year under this suggestion?

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The Answer of Profit Maximization. Samantha Spade & Associates, Ltd. is a small architectural firm located in Portland, Oregon, specializing in the preparation of multi-family residential housing complex, R, and commercial retails, C, architectural designs. Prevailing prices in the market are $10,000 for residential housing designs and $25,000 for commercial retail designs.
Six architects run the firm, and work a 50-hour workweek, 50 weeks per year. They are assisted by six drafting personnel and two secretaries, all of whom work a typical 40-hour workweek, 50 weeks per year. The firm must decide how to target its promotional efforts so as to best use its resources during the coming year. Based on previous experience, the firm expects that an average of 150 hours of architect and 100 hours of drafting time will be required for each residential housing complex design, whereas commercial retail design will require an average of 250 architect hours and 200 drafting hours. Fifty hours of secretarial time will also be required for each architectural design. In addition, variable computer and other processing costs are expected to average $1,000 per residential design and $1,500 per commercial retail design.
A. Set up the linear programming problem the firm would use to determine the profit-maximizing output levels for residential and commercial designs. 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 year for the firm assuming that architects draw a salary of $100,000 per year, drafting personnel earn $65,000 per year, secretaries are paid $20 per hour, and fixed overhead (including promotion and other expenses) averages $50,000.
D. After considering the above data, one senior architect recommended reducing one drafting personnel to part-time status (adjusting salary accordingly) while retaining the rest of the current staff full-time. What are net profits per year under this suggestion?