Profit Maximization: Architect specializing in Residential, R, and commercial, C, designs. Prevailing prices are $10000 for R and $25000 for C. Six architects work 50 hrs/week, 50 weeks/year. Six drafting personnel and two secretaries work 40 hrs/week, 50 weeks/year. The firm expects 150 hrs of architect and 100 hrs of drafting time for each R design, and 250 architect hours and 200 drafting hours for C. Each also requires 50 hours secretarial time per design. In addition, variable processing costs are $1000 per R design adn $1500 per C design.

Set up linear programming to determine proft maximizing output levels for R and C designs. Show both inequality and equality forms of the constraint conditions. Completely solve and interpret the solution values for the linear programming problem. find out maximum possibe net profits per year for the firm assuming architects draw a salary of $100,000 per year, drafting personnel earn $65,000 per year, and secretaries are paid $20 per hour, and fixed overhead averages $50,000.

Finally, after considering all, one drafting personnel is reduced to part time (adjusting salary accordingly) while retaining the rest of the staff full time. What are the net profits under this suggestion?