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forecast and LP based problem

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Problem 1
The personnel manager for a large corporation feels that there may be a relationship between absenteeism and the age of workers. The manager would like to use the age of a worker to develop a model to predict the number of days absent during a calendar year.

Problem 2
The Italian General's Pizza Parlour is a small restaurant catering to patrons with a taste for European pizza. One of its specialties is Italian Prize pizza. The manager must forecast weekly demand for these special pizzas so that he can order pizza shells weekly.

Problem 3
Adele Weiss manages the campus flower shop. Flowers must be ordered three days in advance from her supplier in Mexico. Advance sales are so small that Weiss has no way to estimate the demand for the red roses. She buys roses for $15 per dozen and sells them for $40 per dozen.

Problem 4
The Exeter Company produces two basic types of dog toys. Two resources are crucial to the output of the toys: assembling hours and packaging hours. Further, only a limited quantity of type 1 toy can be sold.

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The solution provides detailed explanation how to work on the forecast question and LP based maximal question.

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Formulate this business case as an LP problem.

The ABC Bicycle Company will be manufacturing both men's and women's models for its Easy-Pedal 10-speed bicycles during the next two months. Management wants to develop a production schedule indicating how many bicycles of each model should be produced in each month. Current demand forecasts call for 150 men's and 125 women's models to be shipped during the first month and 200 men's and 150 women's models to be shipped during the second month. Additional data are shown below:

Labor Requirements (hours)

Model Production Costs Manufacturing Assembly Current Inventory

Men's $120 2.0 1.5 20
Women's $90 1.6 1.0 30

Last month the company used a total of 1000 hours of labor. The company's labor relations policy will not allow the combined total hours of labor (manufacturing plus assembly) to increase or decrease by more than 100 hours from month to month. In addition, the company charges monthly inventory at the rate of 2% of the production cost based on the inventory levels at the end of the month. The company would like to have at least 25 units of each model in inventory at the end of the two months. Formulate this business case as an LP problem.

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