Problem #5 (20 points) A real estate developer is planning to build an office complex. There are three office sizes currently under consideration: small, medium, and large. Small offices can be rented for $600 per month, medium offices can be rented for $750 per month, and large offices can be rented for $1,000 per month. Each small office requires 600 square feet, each medium office requires 800 square feet, and each large office requires 1,000 square feet. The current plot of land available to the developer is 100,000 square feet. The developer wants to ensure that the office complex has at least 3 units of each office size. Moreover, zoning restrictions limit the total number of offices to 50. The developer solved this problem such that he could accrue maximum rent from the small, medium, and large offices he builds. Your job is to analyze this sensitivity report and answer the following questions: Sensitivity Report Adjustable Cells Cell $B$4 $C$4 $D$4 Name Optimal Values Small Optimal Values Medium Optimal Values Large Final Reduced Value Cost 3 0 3 0 44 0 Objective Allowable Allowable Coefficient Increase Decrease 600 400 1E+30 750 250 1E+30 1000 1E+30 250 Constraints Cell Name $E$8 Square footage $E$9 Minimum no. of small $E$10 Minimum no. of medium $E$11 Minimum no. of large $E$12 Total no. of offices Final Value 48200 3 3 44 50 Shadow Price 0 -400 -250 0 1000 Constraint Allowable Allowable R.H. Side Increase Decrease 100000 1E+30 51800 3 41 3 3 41 3 3 41 1E+30 50 51.8 41 a. (2 points) How many small and large offices should the developer build? b. (4 points) What is the total optimal monthly revenue? c. (2 points) If the developer implements the optimal solution, what amount of square footage would remain unused? d. (5 points) What is the impact on the optimal allocation of offices and the objective function value if small offices can be rented for $800 per month rather than $600 per month? e. (2 points) What impact would an increase in 52,800 sq. ft of additional footage have on the optimal objective function value? f. (5 points) What impact will an increase in the monthly rental of small offices to $650 and simultaneous decrease to $800 in the monthly rental of large offices have on the current optimal solution and the objective function value