Optimization problem A multi management company can use 2 fa

Optimization problem

A multi management company can use 2 factories to manufacture a certain product. The fabrication capacity of each factory in regular time is the following:

Factories                        Capacity in units

F-1                                          1800

F-2                                          2200

So the unit cost of production is $0 in regular time at each factory.

The company supplies 3 warehouses whose requests are:

Warehouses                      Unit requests

W-1                                             1500

W-2                                              2000

W-3                                              1800

The overtime manufacturing allows to increase the capacity of 800 units for F-1 and 1000units for F-2. However, we must do a marginal increase in manufacturing costs of 7$ and 6$ for the factories F-1 and F-2, respectively.

The units transportation costs:

                                       Warehouses

                                   W-1       W-2      W-3

Factories   F-1             6              4            7

                 F-2              5              3            2

Formulate the linear model that allows to determine the quantities to manufacture at each factory to minimize the costs(marginal) of fabrication and transport.

Optimization problem A multi management company can use 2 factories to manufacture a certain product. The fabrication capacity of each factory in regular time is the following: Factories Capacity in units F-1 1800 F-2 2200 So the unit cost of production is $0 in regular time at each factory. The company supplies 3 warehouses whose requests are: Warehouses Unit requests W-1 1500 W-2 2000 W-3 1800 The overtime manufacturing allows to increase the capacity of 800 units for F-1 and 1000units for F-2. However, we must do a marginal increase in manufacturing costs of 7$ and 6$ for the factories F-1 and F-2, respectively. The units transportation costs: Warehouses W-1 W-2 W-3 Factories F-1 6 4 7 F-2 5 3 2 Formulate the linear model that allows to determine the quantities to manufacture at each factory to minimize the costs(marginal) of fabrication and transport.

Solution

let x be the quantity manufactured in F1

and y be the quantity manufactured in F2

(x + 800) <= 1800    or x <= 1000

y+1000 <= 2200      or y <=1100

x + y <= 1500

x +y <= 2000

x + y <= 1800

Z = 7x + 6y

Z1 = 6x + 5y

Z2 = 4x + 3y

Z3 = 7x + 2y