Question 1 (25 points)
Answer the questions below and provide justification to obtain full credit for your answers where necessary.
a. What impact does a change in the right-hand side value of a non-binding constraint usually have on the objective function value of a problem?
b. What is the shadow price of a constraint when the constraint has 40 unused hours?
c. What does it imply when a constraint (e.g., labor hours) has a surplus of 10 hours?
d. Name any two techniques that can be classified as an example of decision making under certainty (or also known deterministic modeling). Also provide a practical example of the same.
e. Explain in your own words why integer programming (IP) problems are more difficult to solve than linear programming (LP) problems.
Question 2 (40 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:
Optimal Values Small
Optimal Values Medium
Optimal Values Large