# Statistics

statisticsmath
ATTACHED FILE(S)
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.

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