Page 1 Section 3.2: Linear Programming Problems

May 20, 2018 | Author: Anonymous | Category: Science, Biology, Botany, Plants
Share Embed Donate


Short Description

Download Page 1 Section 3.2: Linear Programming Problems...

Description

Math 141-copyright Joe Kahlig, 10B

Page 1

Section 3.2: Linear Programming Problems Definition: A linear programming problem consists of a linear function to be maximized or minimized subject to certain constraints in the form of linear equations or inequalities.

Set up the following linear programing problems. Do not solve. Example: A landscape company proposes to plant the flower beds for a set of gardens. The company uses three patterns. The number and types of flowers for each pattern are listed in the table. The profit is $30 for Pattern I, $15 for Pattern II,and $25 for Pattern III. company has 800 tulips and 650 daffodils available. The owner of the gardens has stipulated that at least 4 Pattern I be used. How many of each pattern should be used to maximize profit?

Pattern I Pattern II Pattern III

tulips 5 3 4

daffodils 7 4 11

Example: A record store is about to place an order for cassette tapes and compact disks. The distributor from which they order requires that each order must request at least 250 items. The prices that they must pay are $3.50 for each cassette and $7.50 for each compact disk. The distributor also requires that at least 30% of any order be for compact disks. How many cassettes and how many compact disks should the store order so that its total ordering costs will be kept to a minimum?

Math 141-copyright Joe Kahlig, 10B

Page 2

Example: A company manufactures a model G loudspeaker system in plants I and II. The output at plant I is at most 800 systems per month, whereas the output at plant II is at most 600 per month. These loudspeaker systems are shipped to the three warehouses–A, B, and C–whose minimum monthly requirements are 500, 400, and 450, respectively. Shipping costs from plant I to warehouse A, warehouse B, and warehouse C are $16, $20, and $22 per loudspeaker system, respectively, and shipping costs from plant II to each of these warehouses are $18, $16, and $14, respectively. What shipping schedule will enable the company to meet the warehouses’ requirements and at the same time keep its shipping costs to a minimum?

View more...

Comments

Copyright � 2017 NANOPDF Inc.
SUPPORT NANOPDF