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Linear Programming (33 points) Sarah, the CEO of a construction company that renovates buildings, won an auction for an old warehouse in Griffintown, Montreal. The warehouse has a land of 10,000 sqft, and Sarah is interested in building Villas, Apartments, and Offices to sell them. Sarah wants to decide how many sqft to allocate to each type of asset (i.e., Villas, Apartments, and Offices). She has collected data on the revenues, costs, and labor hours that Villas, Apartments, and Offices require per sqft. This information is presented in the following table. Apartments Revenue per sqft $600 Cost per sqft $400 Labor hours per sqft 3.5 Sarah is willing to invest up to $5 million in this project, and the workforce can spend up to 40,640 hours. Borrowing capital is not an option for Sarah. Finally, if Sarah decides to spend less than $5 million on this project, she will earn 3% interest on the remaining capital. Sarah has formulated a linear program to decide how to allocate the 10,000 sqft among the 3 types of assets to maximize the sum of the total revenue and the interest from the remaining uninvested capital. Below you can see the solution of the linear program along with the sensitivity report (from Excel). linear program along with the sensitivity report (from Excel). Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $C$5 gft Villas 1200 0 282 44.05263158 75.5 $D$5 EH Apartments 0 8.204545455 188 8204545455 1E+30 $E$5 g1\"! Ofces 8800 0 206.5 75.5 7.22 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $C$18 Capital 4680000 0 5000000 1 E+30 320000 $C$19 Land Availabil' 10000 76.09090909 10000 6941368421 3226.666667 $C$20 Workforce hours 40640 34.31818182 40640 4693333333 2640 [Note that all the parts of this problem can be solved independently.] Question 20 (3 points) a. What is the optimal solution? (enter your answers in sqft) (3 points) The optimal number of sqft for villas is Question 20 (3 points) a. What is the optimal solution? (enter your answers in sqft) (3 points) The optimal number of sqft for villas is The optimal number of sqft for apartments is The optimal number of sqft for Offices is %] Question 21 (4 points) b. If an external contractor offers Sarah 4,000 additional work hours for $120,000, would you recommend Sarah to accept the offer? 0 Yes O No Question 22 (5 points) c. According to the Excel output, how much money will Sarah earn from interest on the remaining uninvested capital? Enter your answer in dollars. (5 points) Your Answer: :1 Answer Question 23 (9 points) d. What is the objective function in terms of the decision variables? The variables V, A, and O for the number of sqft of Villas, Apartments, and Offices respectively. Enter the corresponding objective coefficients in the blanks (enter numerical answers only). Hint: Do not forget that the company earns interest on the remaining uninvested capital as listed in the text above. XV+ XA+ X 0 + 5150000. maximize z =
