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Linear Programming

Your company keeps fleets of vehicles at a number of sites around the country.


1. Inventory Management

Your company keeps fleets of vehicles at a number of sites around the country. At each site the vehicles can be classified into two types: light and heavy. A heavy vehicle costs more per day, but it can do any task that a light vehicle can do. You would like to determine what mix of vehicles your company should have at each site. If you do not have enough vehicles of the appropriate size to meet the demand on a given day, you must rent the vehicles. Some cost data were collected on the cost of various vehicle types:


Vehicle Type Daily fixed cost Daily variable cost (if used)

Owned Light $32 $40

Owned Heavy $44 $54

Rented Light 0 $175

Rented Heavy 0 $225


At a particular site, your company collected demand data for the number of vehicles required on each of seven days:

Day Lights Heavies

1 6 0

2 3 2

3 5 4

4 8 3

5 2 1

6 4 4

7 1 2

Based on just the above data, what is your recommendation for the number of vehicles to own of each type at this site?  What is your weekly cost?


2. Inventory Depletion


The R. R. Bean Company produces, packages, and distributes freeze-dried food for the camping and outdoor sportsman market. R. R. Bean is ready to introduce a new line of products based on a new drying technology that produces a higher quality, tastier food, so they want to discontinue their current line. The basic ingredients of the current line are dried fruit, dried meat and dried vegetables. There are two products in the current line: the "Weekender" and the "Expedition." In its close-out catalog, the selling prices of the two products are $3.80 and $7.00 per package, respectively. Handling and shipping costs are $1.50 per package for each package, which are provided at no charge. The "Weekender" package consists of 3 ounces of dried fruit, 7 ounces of dried meat, and 2 ounces of dried vegetables. The "Expedition" package has 5 ounces of dried fruit, 18 ounces of dried meat, and 5 ounces of dried vegetables. R. R. Bean would like to deplete its inventories of "old technology" fruit, meat, and vegetables before introducing the new line. The current inventories are 10,000 ounces, 25,000 ounces, and 12,000 ounces respectively of fruit, meat, and vegetables. The book values of these inventories are $2000, $2500, and $1800. Any leftover inventory will be given to the local animal shelter at no cost or benefit to R. R. Bean.  R. R. Bean is confident that it can sell all that it makes of the two products.  What combination of current products should they produce to sell? 


3. Son of Employee Scheduling


Your agency provides telephone consultation to the public from 7 a.m. to 8 p.m., five days a week. The telephone load on your agency is heaviest in the months around April 15 of each year. You would like to set up staffing procedures for handling this load during these busy months. Each telephone consultant you hire starts work each day at either 7, 8, 9, 10, or 11 a.m., works for four hours, is off for one hour, and then works for another four hours. A complication that has become more noteworthy in recent years is that an increasing fraction of the calls handled by your agency is from Spanish-speaking clients. Therefore, you must have some consultants who speak Spanish.

You are able to hire two kinds of consultants: English-speaking only, and bilingual (i.e., both

English- and Spanish-speaking). A bilingual consultant can handle English and Spanish calls equally well. It should not be surprising that a bilingual consultant costs 1.1 times as much as an

English-only consultant. You have collected some data on the call load by hour of the day and language type, measured in consultants required, for one of your more important offices. These data are summarized below:


Hour of the day: 7   8   9   10   11   12   1   2   3   4   5   6   7

English load: 4   4   5    6     6     8    5   4   4   5   5   5   3

Spanish load: 5   5   4    3     2     3    4   3   2   1   3   4   4


For example, during the hour from 10 a.m. to 11a.m., you must have working at least three

Spanish-speaking consultants plus at least six more who can speak English.


How many consultants of each type would you start at each hour of the day?



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