Statistics

Chapter 13 Linear Optimization

Instructions: Please submit your work in one single Excel file with one tab/worksheet for each problem.

1. (50 points) Rosenberg Land Development (RLD) is a developer of condominium properties in the Southwest United States. RLD has recently acquired a 40.625-acre site outside Phoenix, Arizona. Zoning restrictions allow at most eight units per acre. Three types of condominiums are planned: one-, two-, and three-bedroom units. The average construction costs for each type of unit are $450,000, $600,000, and $750,000, respectively. These units will generate a net profit of 10%. The company has equity and loans totaling $180 million dollars for this project. From prior development projects, senior managers have determined that there must be a minimum of 15% one-bedroom units, 25% two-bedroom units, and 25% three-bedroom units.

a. Develop a mathematical model to determine how many of each type of unit the developer should build.

b. Implement your model on a spreadsheet and find an optimal solution.

2. (50 points) Kelly Foods has two plants and ships canned vegetables to customers in four cities. The cost of shipping one case from a plant to a customer is given in the following table.

Plant\Customer	Chicago	Cincinnati	Indianapolis	Pittsburgh
Akron	$1.70	$2.30	$2.50	$2.15
Evansville	$1.95	$2.35	$1.65	$2.95

The plant in Akron has a capacity of 3,500 cases per week, and the Evansville plant can produce 4,000 cases per week. Customer orders for the next week are as follows:

Chicago: 1,200 cases

Cincinnati: 2,000 cases

Indianapolis: 2,500 cases

Pittsburgh: 1,400 cases

Find the minimum cost shipping plan.