- #1

Emilov

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Is there someone who can help mi in formulating two LP models (Thinking) ?

**Example 1**

The Finnish company Suomi Oy produces three products A, B and C. For this, 2 types

of raw materials are used (I and II ). There are 5000 units of I and 7500 units of II

available. See the following table for the raw material requirements per unit:

Raw material requirements:

A B C

I 3 4 5

II 5 3 5

The time needed for each unit of product A is twice that of product B and three times

that of product C. The entire personnel of the company can produce the equivalent of

3000 units. The minimum demand of the three products is 600, 650 and 500 units,

respectively. The ratios of the number of units produced must be equal to 2 : 3 : 4.

Assume the prots per unit of A, B and C as 50, 50 and 80, respectively. Formulate the

problem as LP model in order to determine the number of units of each product that

will maximize the profit.

**Example 2**

Home ltd. produces tables. A table consists of 2 table legs and 1 tabletop. The following

table gives the expected demand for tables in the next 5 years:

Demand: Year 1 Year 2 Year 3 Year 4 Year 5

Tables: 250 200 210 235 200

The next table gives the production times required by each product. There are 2 working

stations that have to be passed. Regular capacity can be increased by overtime. The

maximum overtime is 250 time units per working station and year. One hour overtime

costs 25 monetary units.

Working station 1 Working station 2

Table legs 2 3

Table tops 4 -

Tables - 4

Regular capacity 1500/year 2200/yearInventory holding costs (per unit) are 2 for tabletops, 5 for table legs and 10 for tables.

Initially there are 15 table tops, 14 table legs and 50 tables on stock. Inventory capacity

is 90m3. Table legs, table tops, and tables require 0:5m3, 1m3m, and 2m3m of inventory

space, respectively. Formulate a cost minimizing LP model.Thanks a lot to anyone in advance :)