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Practice 3

Linear Programming

DSO547- Designing Spreadsheet-Based Business Models

1)  Grad & Daughters Insurance carries an investment portfolio of bonds, stocks, and other investment alternatives, such as real estates. At the beginning of next year,   $500,000 will be available to invest in four different alternatives. The expected annual rates of return on these four options are 0.06, 0.09, 0.07, and 0.11. The risk factor per dollar invested is a measure of the inherent uncertainty of the expected   return, so a low risk factor is desirable. The risk factors per dollar invested for the  four investment alternatives are subjective estimates of the possible loss the investor could incur in the worst case analysis (0 means no risk, 1 means the investor could lose everything), which have been provided by a Grad & Daughters analyst. They are 0.02, 0.05, 0.04, and 0.075, respectively. For diversification, no single alternative can be more than $200,000. Management needs a return of at least 0.08, but would like to minimize the risk taken to achieve that return. Find an optimal solution using solver.

2)  A company produces four products with current variable costs of $9, $6.50, $5, and $7.50 per pound, respectively. Because of the company works on a contractual basis with retailers, it knows the demands for each product for the next three months. These are specified in the table. Due to a new labor contract, the variable cost of each of the products will increase by 5 percent at the beginning of month 3. There are currently 50 pounds of each product on hand, and company policy dictates that at the end of the coming three-month period, there must also be in inventory of 50 pounds of each product. These four products share a common bottleneck machine that is available for 320 hours per month (two shifts of eight hours each per day, five days per week, and four weeks per month). Product 1 needs 0.05 hour of the bottleneck machine per pound, product 2requires 0.05 hour/pound, product 3 requires 0.02 hour/pound, and product 4 requires 0.1 hour/pound. The cost of holding inventory per pound per month is 10 percent of the cost of the product. Develop and LP model to meet demand and minimize the cost of production and inventory.

3)  Welz’s Widgets has four production plants, located in Atlanta, Cincinnati, Chicago, and Salt Lake City. It currently has 12 distribution centers, located in Portland, San Jose, Las Vegas, Tucson, Colorado Springs, Kansas City, St. Paul, Austin, Jackson, Montgomery, Cleveland, and Pittsburgh. The monthly capacity  for each plant,monthly demand at each distribution center, and per unit shipping cost from each plant to each distribution canter are given in the table. Welz is interested in minimizing the cost of transporting its widgets from its plants to its distribution centers. Find the minimum monthly cost of shipping?